Exponential Functions - Growth and Decay: Problem 1 (1 point) Exponential Growth and Decay Exponential growth and decay problems follow the model given by the equation A(t) = Pert. . The model is a function of time t A(t) is the amount we have after time t . P is the initial amount, because for t = 0, notice how A(0) = Pelt = Pe = P . r is the growth or decay rate. It is positive for growth and negative for decay Growth and decay problems can deal with money (interest compounded continuously), bacteria growth, radioactive decay, population growth etc. So A(t) can represent any of these depending on the problem. Practice The growth of a certain bacteria population can be modeled by the function A(t) = 400 0.0565t where A(t) is the number of bacteria and t represents the time in minutes. a. What is the initial number of bacteria? (round to the nearest whole number of bacteria.) b. What is the number of bacteria after 5 minutes? | (round to the nearest whole number of bacteria.) C. How long will it take for the number of bacteria to double? (your answer must be accurate to at least 3 decimal places.)The population of Nigeria can be modeled by the function PM = 279(1 + 0.0251]a where P[t) measures the population in millions and t represents the number of years since 2000. 1. Using this model, what was the population of Nigeria in 201m B 2. Predict the population of Nigeria in 2024. D 3. lftnis growth rate continues, in what year will the population of Nigen'a reach 2 billion people? [:] Suppose $10000 is invested at 12% interest compounded continuously. HOW long will it take forthe investment to grow to $20000? Use the model A\") = P3\" and round your answer to the nearest hundredth of a year. It will take [3 years for the investment to reach $20000. \fResearch shows that the radioactive isotope Americium-241 has a halflife of 432.2 years U58 the following if) OOHSiflICt a function that Will model the amount ofAmericium241 remaining alter f MEETS, from an initial amount Of '10 kg. as) = Re" Where (9(3) describes the amount of Americium241 remaining aert years from an initial quantity.r of P kg. WED 2. Horn.r long (in years) will it tat-re for the amount ofAmericium241 remaining to reach 1" kg? C]