An exponential function f(x)=a⋅b^x f(x)=a⋅b^x passes through the points (0, 7000) and (3, 448). What are the values of a and b?

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Q: Suppose that the number of bacteria in a certain population increases according to a continuous…

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Q: What are the  Exponential Curves?

A: Exponential curves is a function in which the variable appeares in theexponent and it grows…

Q: Suppose that the number of bacteria in a certain population increases according to a continuous…

A: Solution :-

Q: What is the total amount of 24000 TL with 4,8 % continuously compound interest after 5 years?

A: Consider the formula for continuous compounding, A=P·er·tHere,P=principalr=rate of interestt=time…

Q: What is the total amount of 4500 TL with 3,7 % continuously compound interest after 3 years?

A: Given Present value (P)= 4500 TL Rate (r)=3.7% Number of years (t)= 3

Q: Suppose the population of a certain bacteria in a laboratory sample is 100. If it doubles in…

A: The initial population of the bacteria is, P0=100. After every t=6, the population doubles. So, the…

Q: odine -131 has a half-life of approximately 8 days. ind the amount of iodine-131 left from a 100…

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Q: Describe Mathematical derivation for graphical assessment of exponential and Weibull Models

A: Here we have to describe Mathematical derivation for graphical assessment of exponential and Weibull…

Q: The rate of a continuous money flow starts at $1000 and increases exponentially at 5% per year for 4…

A: We use the formula                                P = ∫0T f(t)e-rt dt

Q: A population is known to grow exponentially. If it starts at 100 and is 150 after 3 months when will…

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Q: A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into…

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Q: The average profit a local store owner earns on a given day is \$590$590 and is growing…

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Q: Average health premiums have been increasing at a rate of 10%. If an average family's premiums are…

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Q: What rate of interest compounded continuously will yieldan effective interest rate of 6%?

A: It is given that, the effective interest rate is 6%. re=6%=0.06

Q: The accumulated amount of P8000 is P10000 after 2 years, calculate the interest rate if it is…

A: The accumulated amount of $8000 is $10000 after 2 years,   We have to calculate the interest rate…

Q: what is the growth rate of the cells after 6 hours has gone by

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Q: Today there are 500 ants on an colony. They breed with a constant continuous growth rate of 20% per…

A: We will find out the required solution.

Q: A certain quantity Q has initial value 200 and decays by 30% each year. Give an exponential function…

A: Given that, Initial value (a) = 200 Rate of decay (r) = 30%

Q: The rate of a continuous money flow starts at ​$600 and increases exponentially at 4% per year for…

A: Given, Initial amount P0 = $600 R = 4% = 0.04 T = 15 years

Q: Find the time needed to double an investment at 8% annual interest rate compounded continuously.

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Q: A population starts with 2,500 individuals and doubles every 40 years. Give an exponential model for…

A: The initial population is 2500. It gets doubled every 40 years. So after 40 years the population…

Q: Use logarithmic diffenentiation on an alterative method to findthe derivative of the function?

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Q: find the present value of an investment worth $15,000 in 15 years with 5% interest compounded…

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Q: A tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. How do…

A: Consider the given information ,tumor is injected with 0.9gm

Q: Suppose you deposit $4000 at 7% interest compounded continuously. Find the average value of your…

A: Given: Principal amount=$4000 Interest =7% Time = 3 years To find: The average value

Q: What are some of the important characteristics of exponential functions?

A: We need to mention some characteristics of the exponential function. Let's begin.

Q: An investment earns 5.1% yearly interest compounded continuously and is currently growing at the…

A: Solution:Given    i=5.1%     n=1     A=765   To find P=?Formula:A=P(1+i)n

Q: Create two exponential functions that have a horizontal asymptote at y=3 and go through the point…

A: The solution is given below

Q: What exponential function will pass through both (2,4) and (5,7)?

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Q: Determine how long it will take for an initial investment to double if it earns 7% interest per year…

A: The time take to double the initial investment is approximately 10 years  see the calculation below

Q: A computer viruS can grow exponentially just like a real virus in a person's body. Suppose the…

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Q: The population of a pigeons in a city is 6200 and is growing exponentially at 17% per year. Write a…

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Q: Suppose that the number of bacteria in a certain population increases according to a continuous…

A: hourly growth gate of bacteria is 3.045% detailed solution with explanation is given below

Q: Suppose that the number of bacteria in a certain population increases according to a continuous…

A: Given that: The number of bacteria in a certain population increases accordingly according to a…

Q: Suppose you deposit $6000 at 9% interest compounded continuously. Find the average value of your…

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Q: the beginning of the COVID-19 pandemic, the number of new cases was growing exponentially. There…

A: Given query is to find the exponential Moda for COVID cases.

Q: proportional to A, weight W, and height H. A and W measurement values taken from different people…

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Q: At the beginning of the COVID-19 pandemic, the number of new cases was growing exponentially. There…

A: According to the guidelines issued by the company We are supposed to answer only first three…

Q: A freshly inoculated bacterial culture of Streptococcus contains 100 cells. When the culture is…

A: General expression for exponential growth function is given by,                   n(t) = a(1+r)t…

Q: If 26 grams of radioactive waste reduces to 19.35 grams of radioactive waste after 1120 years, then…

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Q: A quantity with an initial value of 510 grows exponentially at a rate such that the quantity doubles…

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Q: An unknown radioactive element decays into non-radioactive substances.  In 660 days the…

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Q: An unknown radioactive element decays into non-radioactive substances. In 880 days, the…

A: The half life of a radioactive element is the time it takes to decay half of its original isotope.…

Q: Suppose that a population that is growing exponentially increases from 800,000 people in 2010 to…

A: the exponential model is of the form, At=A0ekt where A0 original amount of the entity, t is the…

Q: You invest 10,000  and pay 3% interest compound continuously . How will you have in 5 years?

A: Given that You invest 10,000 and pay 3% interest compound continuously .  Now we have to find amount…

Q: Give 5 examples of derivative of exponential function with solution

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Q: $570 is invested in an account earning 5.8% interest (APR), compounded continuously. Write a…

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Q: At the beginning of the COVID-19 pandemic, the number of new cases was growing exponentially. There…

A: Here, the exponential model is given by: P(t)=a×bt...(1) where P(t) is the number of cases after a…

Q: The number of days that elapse between the beginning of the calendar year and the moment a high-risk…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.