Suppose one of your ancestors invested $500 in 1800 in an account paying 4% interest compounded annually. How do you write an exponential function to model the situation?

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Answer 1 · 2018-07-22T14:31:08

$f (t) = 500 {(1.04)}^{t}$ $color(blue)(f(t)=500(1.04)^t)$

The formula for compound interest is given as:

$F V = P V {(1 + \frac{r}{n})}^{n t}$ $FV=PV(1+r/n)^(nt)$

Where:

$F V$ $FV$ is the future value.

$P V$ $PV$ is the present value.

$r$ $r$ is the interest rate as a decimal.

$n$ $n$ is the compounding period.

$t$ $t$ is the time in years.

We have:

$P V = 500$ $PV=500$

$r = \frac{4}{100} = 0.04$ $r=4/100=0.04$

$n = 1$ $n=1$ ( annually )

$F V = 500 {(1 + \frac{0.04}{1})}^{t}$ $FV=500(1+(0.04)/1)^t$

$F V = 500 {(1.04)}^{t}$ $FV=500(1.04)^t$

This is an exponential form:

$f (t) = 500 {(1.04)}^{t}$ $f(t)=500(1.04)^t$