Notes(don't answer the notes) used to answer question 7:

Lesson 3.3: Growth and Decay Discovery Precalculus: A Creative and Connected Approach For each problem in the Exploration.that follows, write an exponential function in the form f(t ) = a.b", where k is a constant, to describe the situation. For parts a-d: identify as ex- ponential growth or exponential decay, domain, range, and sketch a graph. Exploration 3.3.1: An Investigation of Growth and Decay Models a. Write a function F(t) that describes the value after t years of a $2000 b. Write a function V(t) that describes investment that increases by 9% per the value after t years of a $25,000 year. car that depreciates (loses value) at a rate of 15% per year. c. Write a function P (t) that describes d. Write a function m (t) that describes the population after t days of a the remaining mass after t years colony of 1000 fire ants that doubles of a 100-gram sample of a radioac- in population every 13 days. tive compound with a half-life of 31 years. e. For your function in Part a above, f. For the function in Part a, solve find the value of your investment to find how long it would take to double your original investment. Try after 10 years. to solve this equation without using a graph or table. What problem do you encounter? h. Simplify the function from Explora- tIn 2 g. For the function in Part c, solve to find how long it would take for the tion 3.2.1, N(t) = Noe " , to show ant population to reach 10,000. that the function can be written in the form f (t) = a.bk .Lesson 3.3: Growth and Decay Discovery Precalculus: A Creative and Connected Approach For each problem in the Exploration.that follows, write an exponential function in the form f(t ) = a.b", where k is a constant, to describe the situation. For parts a-d: identify as ex- ponential growth or exponential decay, domain, range, and sketch a graph. Exploration 3.3.1: An Investigation of Growth and Decay Models a. Write a function F(t) that describes the value after t years of a $2000 b. Write a function V(t) that describes investment that increases by 9% per the value after t years of a $25,000 year. car that depreciates (loses value) at a rate of 15% per year. c. Write a function P (t) that describes d. Write a function m (t) that describes the population after t days of a the remaining mass after t years colony of 1000 fire ants that doubles of a 100-gram sample of a radioac- in population every 13 days. tive compound with a half-life of 31 years. e. For your function in Part a above, f. For the function in Part a, solve find the value of your investment to find how long it would take to double your original investment. Try after 10 years. to solve this equation without using a graph or table. What problem do you encounter? h. Simplify the function from Explora- tIn 2 g. For the function in Part c, solve to find how long it would take for the tion 3.2.1, N(t) = Noe " , to show ant population to reach 10,000. that the function can be written in the form f (t) = a.bk .Question 7 10 pts In Exploration 3.3.1 the constant k was addressed in the exponential parent function f (I) = a . but Which is the strongest justification of how k affects an exponential function? O The k value scales the initial amount. O The k value shifts the graph left or right. O The k value scales the input to adjust for the unit of time. O The k value shifts the graph up or down.Question 8 10 pts In Exploration 3.3.1, you wrote equations for some growth and decay models. Using the equation obtained from part c, what was your answer to part g ("solve to find how long it would take for the ant population to reach 10,000") to the nearest day? 43