# Consider the exponential function f(x)=1,250cdot1.08^x which models the amount of money

Consider the exponential function $f\left(x\right)=1,250\cdot {1.08}^{x}$ which models the amount of money invested in a bond fund where x represents the number of years since the money was invested. a. What is the rate of growth or decay?
b. What does 1,250 represent?

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Solution:
$f\left(x\right)=1250×\left(1.08{\right)}^{x}\to$ (1)
where x represent the number of years.
The formula for exponential growth of a variable y at the growth rate r, as time x goes on indiscrete intervals (that is, at integer times 0,1,2,3,...), is ${y}_{x}={y}_{0}\left(1+r{\right)}^{x}\to$ (2) where ${y}_{0}$ is the value of y at time 0.
a) On comparing (1) and (2) we have
$1.08=1+r$
$\therefore r=1.08-1$
$r=0.08=\frac{8}{100}=8\mathrm{%}$
Therefore rate of growth =8% per year
b) 1250 represents the amount of money invested at time x=0
That is the initial amount invested in the bond fund.