14: Math 112 Written Homework: Exponential and Log Applications Student Name:____________________________________________ Instructor: J.M.S. Liston Math 112 Section:________ Directions: ANSWER THE FOLLOWING QUESTIONS ON YOUR OWN BLANK, WHITE PAPER (e.g. printer paper). Begin by first stating what you know, then what you're trying to find; be sure to SHOW ALL WORK to reflect your thinking and calculations. Explanations should be given in complete sentence (i.e., subject and verb). If you solve with a graph, it should be drawn accurately, SCALED, both axes identified with units. Staple this page to the TOP of your work. Be sure to put your name on all submitted pages. Failure to follow these instructions will result in a lower grade. 1. Suppose Matt initially invests $3000 in an account bearing 4% interest compounded monthly. How long will it take for the deposit to double in value? Round to the nearest 0.01 year. 2. A certain lake is stocked with 1000 fish. The population is growing according to the logistic curve: 10,000 P 1 9e 0.2 t where t is measured in months since the lake was initially stocked. After how many months will the fish population be 2000? Round to the nearest 0.01 month. Is there a maximum possible fish population that the lake can sustain? 1. $4,000 is invested in an account bearing 8% interest compounded continuously. The amount of time it takes for the money to grow by a factor of x is given by t=f ( x)=8 ln (x) . (For example, the amount of time required for the investment to double is f (2)=8 ln (2) . How long will it take the balance in the account to 1 reach $6,000? Find a formula for the inverse function. Evaluate f ( 8) and explain what this tells you in practical terms