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

Question

Consider the exponential function $f (x) = 1, 250 \cdot {1.08}^{x}$ 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?

Answer 1

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

∴ 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.

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

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