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?

You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

coffentw
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.