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F(t)=1,500(1.045)^(t)
The future value in dollars,
F(t), of an investment after
t years is given by the function defined. What is the initial value of the investment in dollars?

$F(t)=1,500(1.045)^{t}$ $\newline$ The future value in dollars, $F(t)$ , of an investment after $t$ years is given by the function defined. What is the initial value of the investment in dollars?

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Write exponential functions: word problems

Full solution

Q.

F(t)=1,500(1.045)^{t}

\newline

The future value in dollars,

F(t)

, of an investment after

t

years is given by the function defined. What is the initial value of the investment in dollars?

Identify initial value: Identify the initial value in the function. $\newline$ The function $F(t) = 1,500(1.045)^{t}$ represents the future value of an investment after $t$ years. The initial value of the investment is the value when $t = 0$ , which is the constant term in the function before any growth has occurred due to the interest rate.
Calculate initial value: Calculate the initial value by substituting $t = 0$ into the function. $\newline$ $F(0) = 1,500(1.045)^{(0)}$ $\newline$ Since any number raised to the power of $0$ is $1$ , we have: $\newline$ $F(0) = 1,500(1) = 1,500$
Verify calculation: Verify the calculation. $\newline$ $1,500(1.045)^{(0)} = 1,500 \times 1 = 1,500$ $\newline$ There is no math error in the calculation.

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