Solve these real life problems using exponential functions C. Solve these real-life problems using exponential functions.1. A population starts with 1,000 individuals and triples every 80 years. (a) Give an exponential modelfor this situation. (b) What is the size of the population after 100 years?2. Suppose that the half-life of a substance is 250 years. If there were initially 100 grams of thesubstance, (a) give an exponential model for this situation. (b) How much will remain after 500 years?3. P10,000 is invested at 2% compounded annually. (a) Give an exponential model for this situation. (b)What is the amount after 12 years? Exponential FunctionAn exponential function with base b is a function of the form f(x) = b* or y = b*,where b > 0, b + 1.%3DMany applications involve transformations of exponential functions. Some of the most common applications inreal life of exponential functions and their transformations are population growth, exponential decay, andcompound interest.Example. Let t = time in days. At t = 0, there were initially 20 bacteria. Suppose that the bacteria doublesevery 100 hours. Give an exponential model for the bacteria as a function of t.Given: T100 hours, y = 20 bacteriaSolution:Exponential Models and Population GrowthSuppose a quantity y doubles every T units of time. If yo is the initial amount, thenthe quantity y after t units off time is given by y = yo(2)'/".Anexponentialfor thismodelsituationis%3Dy = 20(2)/100%3D

1) Given: y0=1000 T=80 years t=100 years The mathematical model for population…

ms using exponential functions. 1. A population starts with 1,000 individuals and triples every 80 years. (a) Give an exponential model for this situation. (b) What is the size of the population after 100 years?

ms using exponential functions. 1. A population starts with 1,000 individuals and triples every 80 years. (a) Give an exponential model for this situation. (b) What is the size of the population after 100 years?

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter4: Exponential And Logarithmic Functions

Section: Chapter Questions

Problem 12CC: Suppose that the initial size of a population is n0 and the population grows exponentially. Let n(t)...

See similar textbooks

Related questions

Q: 2. A bell is struck and the volume, which was recorded at 90 decibels, decreases at a constant rate…

A: a= initial sound= 90 decibelsIt decreases 9.8% per second. 9.8%=0.098Sp after 1 second sound is…

Q: A chemical degrades over time, and the amount of chemical present in a sample is an exponential…

A: Given that the half-life of the chemical is 6 years. Here the quantity is decreasing with the time.…

Q: The initial population of pika in a region is 144 pikas. The pika population is decreasing by 8%…

Q: A population numbers 19,000 organisms initially and decreases by 5.2% each year. Suppose P…

Q: 4. Population of a particular species in a lab is 350. If they grow in an exponential pattern at the…

Q: A population numbers 18,000 organisms initially and grows by 2.5% each year. Suppose PP represents…

Q: inheritance of $15,000 is invested at a rate of 3.2% compounded continuously What is the value of…

Q: Carbon-14 is a radioactive element with a half-life of about 5,730 years. Carbon-14 is said to decay…

A: Given Information: The decay rate of carbon 14 = 0.000121

Q: A population numbers 10,000 organisms initially and decreases by 4.8% each ye Suppose P represents…

A: Given data: The initial population of the organism is P0=10,000. The given rate at which the…

Q: A population numbers 18,000 organisms initially and grows by 17.9% each year. Suppose P represents…

Q: A population numbers 13,000 organisms initially and grows by 13.9% each year. Suppose P represents…

A: To determine: An exponential model for the population that can be written in the form P=a·bt Given:…

Q: A species of beetles grows 41% every year. Suppose 100 beetles are released into a field construct…

Q: Radon-22 decays continously at a rate of 17.3% per day. Suppose the scientist begins with a sample…

A: Giveninitial amount or Radon-22(Rn0)=300 mgrate of decay(r)=-17.3% per day =- 0.173 per day(negative…

Q: A certain population is initially 5000 and declines by 8% per year. a) Find an exponential formula…

A: Given: Population is initially= 5000 declines by 8% per year.

Q: 10. A population is declining at a continuous rate of 3% per day. If there were 20 in the population…

A: Question- 10. A population is declining at a continuous rate of 3% per day. If there were 20 in the…

Q: 3. P10,000 is invested at 2% compounded annually. (a) Give an exponential model for this situation.…

Q: A population grows according to an exponential growth model. The initial population is Po=4, and the…

Q: A tube of toothpaste is found to have 113 bacteria present one month after it was bought and 559…

A: Let the exponential model be written as,

Q: 1. The earth's atmospheric pressure, P, in terms of height above sea level, is often modeled by an…

A: Given the Pressure P (in millibar) decrease exponentially with height h (kilometers). Hence : P(h) =…

Q: A population numbers 11,000 organisms initially and decreases by 2.4% each year. Suppose P…

A: Initially the number of organism is a=11000 and it is decreasing by 2.4% each year. After first…

Q: 9) The half-life of Erbium-165 is 10.4 hours. After 41.6 hours, a sample of Erbium-165 has reduced…

A: Half life of Erbium-165 is 10.4 hours.

Q: A certain quantity Q has an initial value of 7 and decays by 4% each year. Give an exponential…

Q: A population numbers 17,000 organisms initially and grows by 16.4% each year. Suppose P represents…

Q: The rate of auto thefts doubles every 9 months. (a) Determine, to two decimal places, the base b for…

Q: A bacterial population flows the “law of exponential change". If between noon and 2:00 PM the…

A: image is attached

Q: A population numbers 11,000 organisms initially and grows by 18% each year. Suppose P represents…

A: The initial population of organisms was 11,000. It grows by 18% each year. This basically means…

Q: The number of bacteria in a culture is increasing according to the law of exponential growth. After…

Q: A species of frogs population grows 24% every year. Suppose 100 frogs are released into a pond.…

A: Given Growth rate R=24% Initial number of frogs P0=100

Q: A tube of toothpaste is found to have 58 bacteria present one month after it was bought and 414…

A: Let B0 represents the number of bacteria present in the toothpaste at the time of purchase. Then,…

Q: A colony of bacteria with an initial population of 3000 grows over time t (in hours) at a rate of…

A: We use here simple exponential growth and decay function to solve these problems.

Q: A population numbers 19,000 organisms initially and grows by 2.7% each year. Suppose P represents…

A: A number of population 19000. The rate of increasing population is 2.7% per year and ''t'' be the…

Q: 11. The population of a region is growing exponentially. There were 30 million people in 1950 (when…

Q: A population numbers 12,000 organisms initially and grows by 14.9% each year. Suppose PP represents…

A: Given Initial population of organisms = 12000 And growth rate = 14.9 % per year

Q: A population numbers 10,000 organisms initially and decreases by 3% each year. Suppose PP…

A: A population numbers 10,000 organisms initially and decreases by 3% each year. The general equation…

Q: A report tells us that in 2019 there were 800 of a certain type of animal in an area, but that the…

A: Question : A report tells us that in 2019 there were 800 of a certain type of animal in an area,…

Q: 33) A population of 950 bacteria grows continuously at a rate of exponential function, N(t), that…

A: The continuous exponential growth model is defined as- y=aekt where, a is initial value, k is growth…

Q: A population numbers 11,000 organisms initially and grows by 8.7% each year. Suppose P represents…

A: An exponential growth model is modeled by the function, P=abt Here, a is the initial value of the…

Q: A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has…

Q: A population numbers 19,000 organisms initially and decreases by 2.3% each year. Suppose P…

Q: A population numbers 15,000 organisms initially and decreases by 2.6% each year. Suppose PP…

Q: 12. Under ideal conditions, a population of rabbits has an exponential growth rate of 11.7% per day.…

A: Here we will find the time in days to have 500,

Q: A population numbers 20,000 organisms initially and grows by 3% each year. Suppose P represents…

A: Initial population Pi = a = 20,000 Increasing rate r = 3% = 3/100 = 0.03 time = t P = a*bt

Q: A population P is initially 1,000. Find an exponential model (growth or decay) for the population…

A: Given, A population P is initially 1,000. Find an exponential model (growth or decay) for the…

Q: A population numbers 16,000 organisms initially and grows by 2% each year. Suppose P represents…

A: Find population after t years from the given data.

Q: 25. The decay of a radioactive substance can be represented by more than one exponential model.

Q: Using the concept of exponential growth and exponential decay. Solve the given problem. 1. A small…

A: Exponential equation of the form Where P(x) represents the population after x years and ‘a’…

Q: A population numbers 13,000 organisms initially and grows by 18.4% each year. Suppose P represents…

A: We know that,The exponential growth equation with rateof growth r in time period t is given…

Q: 2. Suppose that the half-life of a substance is 250 years. If there were initially 100 grams of the…

A: We have to find the half life and the compound intrest in two problems.

Q: The half-life of radium-226 is 1620 yr. Given a sample of 1 g of radium-226, the quantity Part: 0/2…

A: Given query is to convert the modal into e base exponential modal.

Q: A population numbers 12,000 organisms initially and decreases by 1.8% each year. Suppose Prepresents…

Question

Solve these real life problems using exponential functions

Exponential Function
An exponential function with base b is a function of the form f(x) = b* or y = b*,
where b > 0, b + 1.
%3D
Many applications involve transformations of exponential functions. Some of the most common applications in
real life of exponential functions and their transformations are population growth, exponential decay, and
compound interest.
Example. Let t = time in days. At t = 0, there were initially 20 bacteria. Suppose that the bacteria doubles
every 100 hours. Give an exponential model for the bacteria as a function of t.
Given: T
100 hours, y = 20 bacteria
Solution:
Exponential Models and Population Growth
Suppose a quantity y doubles every T units of time. If yo is the initial amount, then
the quantity y after t units off time is given by y = yo(2)'/".
An
exponential
for this
model
situation
is
%3D
y = 20(2)/100
%3D

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1 As per guidelines we are solving one question.Please re-post other questions.

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Use a graphing calculator to solve each problem. In Example 4, suppose that a birth control program changed the formula for poulation growth to Pt=1000e0.01t. How long will the food supply be adequate? EXAMPLE 4 Using a Graphing Calculator to Solve a popuiation Problem Suppose that a country with a population of 1000 people is growing exponentially according to the population function Pt=1000e0.02t Where t in years. Furthermore, assume that the food supply, measured in adequate food per day per person, is growing linearly according to the function fx=30.625x+2000 In how many years will the population outstrip the food supply?
Suppose that the initial size of a population is n0 and the population grows exponentially. Let n(t) be the size of the population at time t. (a) Write a formula for n(t) in terms of the doubling time a. (b) Write a formula for n(t) in terms of the relative growth rate r.
Suppose that $12,000 is invested in a saving account paying 5.6% interest per year. (a)Write the formula for the amount in the account after t years if interest is compounded monthly. (b)Find the amount in the after 3 years if interest is compounded daily. (c)How long will it take for the amount in the account to grow to $20,000 if interest iscompounded continuously?
With what kind of exponential model would doubling time be associated? What role does doubling time play in these models?
With what kind of exponential model would half-life be associated? What role does half-life play in these models?