Question

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

Exponential models

Consider the exponential function $$f(x)=1,250\cdot1.08^x$$ 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?

2021-02-01
Solution:
$$f(x)=1250\times(1.08)^x\to$$ (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 $$y_x=y_0(1+r)^x\to$$ (2) where $$y_0$$ is the value of y at time 0.
a) On comparing (1) and (2) we have
$$1.08=1+r$$
$$\therefore r=1.08-1$$
$$r=0.08=\frac{8}{100}=8\%$$
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.