The area covered by a certain population of bacteria increases according to a continuous exponential growth model. Suppose that a sample culture has an initial area of 1.9 mm" and an observed doubling time of 4 minutes. (a) Let : be the time (in minutes) passed, and let y be the area of the sample at time t. OIno Write a formula relating y to t. Use exact expressions to fill in the missing parts of the formula. Do not use approximations. (b) What will the area of the sample be in 5 minutes? Do not round any intermediate computations, and round your answer to the nearest tenth.

Q: Suppose $5,000 is invested at 7% intrest compounded continiously. How long will it take the…

A: The investment amount P = $ 5000. The interest rate r = 7% compounded continuously. The final amount…

Q: Suppose $500 is deposited into an account paying interest at a rate of 7%, continuously compounded.…

A:

Q: How many years will it take for an initial investment of $60,000 to grow to $90,000? Assume a rate…

A: Initial investment P = $ 60,000, Final amount A = $ 90,000, Rate of interest = 18 % = 0.18

Q: Find the amount resulting in 12 years, if $25,000 is invested now at an interest rate of 4.25% p.a.…

A: Given that, P=25000, r=4.25%, t=12years

Q: Suppose $500 is deposited into an account paying interest at a rate of 7%, continuously compounded.…

A: Given, Suppose $500 is deposited into an account paying interest at a rate of 7% continuously…

Q: Find the time required for an initial investment of $2000 to reach $3500 if the interest is…

A: Topic- continuous compound interest

Q: How many years will it take for an initial investment of $30,000 to grow to $75,000? Assume a rate…

A: An initial investment (P) compounded continuously with a rate of interest (r) in time (t) will grow…

Q: The amount of carbon 14 remaining in a sample that originally contained A grams is given by C(t) =…

A: The amount of carbon 14 remaining in a sample that originally contained A grams is given bt…

Q: al Intal 5. What is the annual percentage yield for money invested at an annual fate UI 0.0820…

A:

Q: An initial amount of $1900 is invested in an account at an interest rate of 8% per year, compounded…

A:

Q: A certain hermit wants to design a reactor using radioactive material A that will be converted into…

A:

Q: How long (in years) will it take a $200 investment to be worth $300 if it is continuously compounded…

A:

Q: How many years will it take for an initial investment of $20,000 to grow to $50,000? Assume a rate…

A: The principal amount, P = $20,000 Future amount, A = $50,000 Rate of interest, r = 11% = 0.11 To…

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: If f(x) and g(x) is any function then, If limx→∞f(x)g(x)=∞ then f(x) grows faster than g(x). If…

Q: How long (in years) will it take a $200 investment to be worth $300 if it is continuously compounded…

A:

Q: 2. Assuming no withdrawals during the investment, how many years will it take for $500, invested at…

A:

Q: Suppose that a chemical reaction proceeds according to the law of growth and decay. If half the…

A:

Q: How long will it take to triple $12000, invested at 4.5% compounded continuously? (A = Pe*t) %3D

A: We are given the initial value to be $12000 and rate r = 4.5% = 0.045. Now, we need to find that how…

Q: At what nominal rate compounded continuously must money be invested to double in 6 years? A rate of…

A: We will solve the problem

Q: How long, to the nearest year, will it take an investment to triple if it is continuously compounded…

A: Formula to calculate continuously compounded interest: A = Pert where, A is Amount at time t,P =…

Q: How long (in years) will it take a $300 investment to be worth $400 if it is continuously compounded…

A:

Q: A CERTAIN RADIOACTIVE MATERIAL IS KNOWN TO DECAY AT A RATE PROPORTIONAL TO THE AMOUNT PRESENT. IF…

A: Given that, after one hour, the 10% of the material is decayed. find the expression of the material…

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: Suppose the population of certain fungi in a laboratory sample is 12. (A) If it quintuples in…

A:

Q: If the half-life of a radioactive substance is 5,200 years, then at what rate is it decaying? (Hint:…

A:

Q: The number of bacteria in a certain population increases according to a continuous exponential…

A: In this question we have to find how many hours does it take for the size of the sample to double.

Q: A money market fund has a continuous flow of money at a rate of f(x)=0.07x+100 for 10 years. Find…

A:

Q: How long (in years) will it take a $200 investment to be worth $900 if it is continuously compounded…

A: We need to find time when $200 will be worth $900.

Q: Find the present value Po of each amount P due t years in the future and invested at interest rate…

A: Given: The amount P= $100,000 The time is t= 6 years. The rate of interest is k=3%

Q: A mold population is growth at 8% every three months. If there is initially 3 cm3 of mold, when will…

A: Formula for population growth is  P=P0ert where P = final population after time t P0 = initial…

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: Following the birth of a child, a parent wants to make an initial investment P, that will grow to…

A: Given Initial amountP=P0 Interest rater=6%=0.06 Time t=18 years Future valueA=70,000

Q: If $12, 000 is invested at a rate of 3% per year compounded continuously, find value of the…

A: The formula for continuously compounded interest is, A=Pert where P is the principal amount, r is…

Q: How many years will it take for an initial investment of $20,000 to grow to $70,000? Assume a rate…

A:

Q: If the half-life of a radioactive substance is 6,700 years, then at what rate is it decaying? 1…

A: The decay law is given by, A(t)=A0e-kt Where, A0 is the amount at t=0. And, t1/2=ln2k

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

A: Given,

Q: Suppose that money is deposited daily into a savings account at an annual rate of $900. If the…

A:

Q: Suppose that P0 is invested in a savings account where interest is compounded continuously at 3.1%…

A:

Q: A company is considering expanding their production capabilities with a new machine that costs…

A: Cost of new machine = 53,000 Investment = 53000 Rate of interest, r= 0.7% per year = 0.007 Time = 9…

Q: how many years will it take for an initial investment of $50,000 to grow to $75,000? Assume a rate…

A:

Q: An initial amount of $1800 is invested in an account at an interest rate of 7% per year, compounded…

A:

Q: 3. What will happen to Joshua's money if his money will be 6.33% compounded continuously for 17.36…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 6. Find dthe time required for an investment of $10,000 to grow to $18,000 at an annual interest…

A: 6) Given: P=$10,000, A=$18,000 and r=6%=0.06. The Compound Interest Formula is given by,  A=P1+rnnt…

Q: How long (in years) will it take a $900 investment to be worth $1000 if it is continuously…

A: Amount = $1000 Principal=$900 Interest rate = 8%

Q: consider an investment where $42000 is invested for 15 years at 6% compounded continuously. how much…

A: Given  Invested amount = $42000 interest rate = 6 % compounded continuously  time = 15 years

Q: how long will it take an investment of $25,000 to grow to $35,000 ast an anual interest rate of 5%…

A:

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

A:

Q: If a population of is becoming extinct and the population is decaying exponentially. Assume that…

A: From given information

Q: How many years will it take for an initial investment of $20,000 to grow to $30,000? Assume a rate…

A: Consider the Initial amount P=$20000. Final amount A=$30000. Rate of interest r=12%=0.12 The…

Q: How many years will it take for an initial investment of $30,000 to grow to $75,000? Assume a rate…

A: We will solve the following.