2) During the exponential phase, E. coli bacteria in a culture increase in number at a rate proportional to the current population. If the growth rate is 1.9% per minute and the current population is 172.0 million, what will the population be 7.2 minutes from now?

Q: 3. An account with an initial deposit of $6,500 earns 7.25% annual interest, compounded…

A:

Q: If $6000 is invested at 3% compounded continuously, what is the amount after 8 years? The amount…

A: Answer  is   7625

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

A:

Q: Suppose a new mosquito-borne virus has emerged and has caused 550 cases to- date. The number of…

A: The exponential function of t is given below: A=A0e-ktWhere, k=rate, t=time

Q: If I invest $25,000 in a savings account with a 5.75% interest rate which is compounded…

A:

Q: How much money needs to be deposited now into an account to obtain $3,300 in 14 years if the…

A:

Q: Verify that the half-life of a quantity that decays exponentially with decay constant k is equal to…

A: Given : Quantity decays exponentially with constant decay constant k. The standard exponential…

Q: 1. Suppose a population of rabbits starts with 30 rabbits. 60 days later, the population is 120…

A:

Q: A population of kangaroos is growing at a rate of 2% per year, compounded continuously. If the…

A: Given growth rate = 2% Let current population be x So final population = 150% of x Continuous…

Q: 1. A certain species of virus is increasing in number exponentially every hour. The initial virus…

A: To find growth rate of the virus.

Q: For an exponentially growing quantity that grows at a rate of 4.0% per year, approximate the number…

A: topic - exponential function

Q: 1. During the exponential phase, E. coli bacteria in a culture increase in number at a rate…

A: It is given that coli bacteria in a culture increase in number at a rate proportional to the current…

Q: Suppose that the half-life of a cesium is 30 years. If there were initially 1000 g of the substance…

A:

Q: An account now contains $3,670 and has been accumulating interest at 5% annual interest, compounded…

A: We have to find the amount in the account 5 years ago.

Q: 1. Suppose that a couple invested P50, 000 in an account when their child was born, to prepare for…

A: NOTE: As Per our guidelines, I have solved first problem.   P be principal amount A be the final…

Q: (3) Suppose an experiment was conducted to identify the exponential growth model of a species of…

A: As per the company rule, we are supposed to solve one problem from a set of multiple problems.…

Q: 2) Carbon-14 decays or emits a radioactive particle at a regular and consistent exponential rate and…

A:

Q: How many years will it take $1,000 to grow to $1,900 if it is invested at 3.50% compounded…

A:

Q: 2. Suppose a population of insects increases according to the law of exponential growth. There were…

A: We will solve the problem

Q: A bank offered 1 3/4% interest on savings accounts compounded continuously. -How much is a $5,000…

A:

Q: A Bank offered 1 3/4% interest on savings accounts compounded continuously. How much is a $5000…

A: The formula used for evaluating the amount accumulated on the amount saved in the bank compounded…

Q: Find the exponential growth equation for a population that doubles in size every unit of time and…

A: Given: At time, t=0, No. of individuals=20.

Q: The population of a certain community follows the law of exponential change. If the present…

A: Topic = Algebra

Q: suppose that the half-life of a cesium in 30 years.if there were initially 1000g of the substance.(…

A: The radioactive decay is modelled using the formula: N(t)=N0e-kt, where N0 is the initial amount and…

Q: 8) A bacterial culture has an initial population of 10,000. If its population declines to 3000 in 8…

A: Exponential model of population is given by,     P(t) = Po * e^(kt).

Q: Consider a population that begins growing exponentially at a base rate of 4.1​% per year and then…

A: Given that a population is begins growing exponentially at a base rate of  r=4.1% per year and then…

Q: At what nominal rate compounded continuously must money be invested to triple in 6 ​years?

A: Formula for continuously compounded is given by A=Pert Where A is total amount P is Principal Amount…

Q: How many years will it take $9,000 to grow to $17,200 if it is invested at 2.75% compounded…

A:

Q: 1. The amount of a certain medicine in the bloodstream decays exponentially with a half- life of 5…

A: Here, given that the amount of certain medicine in the bloodstream decays exponentially with a…

Q: 1. A certain species of virus is increasing in number exponentially every hour. The initial virus…

A: We will apply exponential growth formula to solve this question

Q: 9. The number of bacteria in a Petri dish grows exponentially, starting with just 1 bacterium, but…

A:

Q: A ranch experienced growth of its gopher population at a 1.5% annual rate, compounded continuously.…

A: Exponential growth function =A = Pert → 1Given A = 78        r = 1.5% = 1.5100…

Q: practice question 18

A: P0= Initial amount = 2700r= interest rate = 6.8% =0.068t= time = ?P(t)= Final amount = 2700 times 2=…

Q: The population of a southern city follows the exponential law. if the population doubled in size…

A: Explanation of the solution is given below...

Q: Questlon 1 Given an interest rate of 7.2% per year, compounded continuously. What is the quarterly…

A:

Q: How long will it take a $500 investment to be worth $700 if it is continuously compounded at 10% per…

A:

Q: If $6,000 is invested at 3% compounded continuously, what is the amount after 7 years? The amount…

A:

Q: How long would $8600 have to be invested into a fund earning 8.1% interest, compounded cotinuously,…

A: Continuous compound interest:

Q: How much money should be invested at a rate of 6% compounded continuously to produce an amount of…

A:

Q: 14. The current population of a town is 50,000 and is growing exponentially. If the population is…

A: Please refer the attached image for complete solution.

Q: How much should you invest now (to the nearest dollar) in an account that earns interest at a rate…

A: Given: Amount after 15 years=$11,000 Rate of interest compounded continuously=6.4% To find: Amount…

Q: If the population of a country is 100 million people and the population is increasing exponentially…

A:

Q: suppose $5,000 is invested in an account at an annual interest rate of 3.7% compounded continuously.…

A: Given,

Q: How much money must be invested now at 10% interest compounded continuously so that $120,000 will be…

A:

Q: If 2000 dollars is invested in a bank account at an interest rate of 9 per cent per year, compounded…

A:

Q: If 8000 dollars is invested in a bank account at an interest rate of 9 per cent per year, compounded…

A:

Q: 2. The population of a suburb doubled in size in an 18-month peri growth continues and the current…

A: In this question we will use basic of calculus i.e application of differential equation. We will…

Q: How long does it take an investment to triple at an annual interest rate of 6.45% compounded…

A:

Q: 1. Initially, there are 150 grams of radioactive element and in 2550 years there will be 60 grams…

A:

Q: If the half-life of a radioactive substance is 7,300 years, then at what rate is it decaying? (Hint:…

A:

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.