Question

TWO QUESTIONS NEED HELP PRONTO

1. Describe how each of the numbers in the function g(x) = .24(2)^x+3 - 4 transforms the graph of f(x) = 2^x.



2. You have 2 options to invest some money in an account. The first account, you can invest $100 with an interest rate of 3%, using the equation y = 100(1.03)^x. In the second account, you can invest $125 with an interest rate of 1.5%, using the equation y = 125(1.015)^x. If x is representing time in years and y represents the total amount of money in the account, which account would earn you more after 15 years?



Be sure to show your work and explain everything thoroughly!

Answer 1

The transformation from g(x) to f(x) includes

• Translate to the right 3 units

• Translation of 4 units up

• A vertical compression of 1/24

Using the equation y = 100(1.03)ˣ will earn more

How to describe the transformation

The function g(x) = 24(2)ˣ⁺³ - 4 transforms to the graph of f(x) = 2ˣ following the procedures stated

g(x) = 24(2)ˣ⁺³ - 4

Translate to the right 3 units, so we have g(x) = 24(2)ˣ - 4

Translation of 4 units up, so we have g(x) = 24(2)ˣ

Apply a vertical compression of 1/24, so we have g(x) = (2)ˣ = f(x) = 2ˣ

Comparison to find a the account that will earn more

For x = 15

y = 100(1.03)¹⁵ = 155.8

y = 125(1.015)¹⁵ = 149.49