When Tyler was born, his father created a college fund by opening an investment account with $3,500 and an annual interest rate of 2.85%. The current amount of the investment account can be modeled by an exponential function in the form f(x)=a⋅bx

Question

, where x is the number of years after the investment started. Find the function f(x)
.(1 point)
Responses

f(x)=3,500⋅1.285x
f left parenthesis x right parenthesis equals 3,500 times 1.285 superscript x baseline

f(x)=3,500⋅0.715x
f left parenthesis x right parenthesis equals 3,500 times 0.715 superscript x baseline

f(x)=3,500⋅2.85x
f left parenthesis x right parenthesis equals 3,500 times 2.85 superscript x baseline

f(x)=3,500⋅1.0285x

Answer 1

To find the function \( f(x) \) that models the growth of the investment account, we start with the initial investment and the annual interest rate.

• The initial investment (\( a \)) is $3,500.
• The annual interest rate is 2.85%, which as a decimal is \( 0.0285 \).
• The growth factor \( b \) for the investment account would be \( 1 + \) interest rate. Therefore: \[ b = 1 + 0.0285 = 1.0285 \]

Now we can express the function in the form:

\[ f(x) = a \cdot b^x = 3500 \cdot (1.0285)^x \]

So the correct answer is:

\[ f(x) = 3,500 \cdot 1.0285^x \]

This is represented in your responses as:

f(x) = 3,500⋅1.0285^x.