Question

Exponential growth/decay problem 1

Answer 1

a) growth

b) $500

c) 6% = 0.06

d)
`f(x)=500(1.06)^x`

e) $595.51

Explanation:

Part (a)

Exponential GROWTH, since interest is applied to the account each year.

Part (b)

Initial amount = $500

Part (c)

Growth factor = 6% = 0.06 (in decimal form)

Part (d)

General form of exponential growth function:

`f(x)=a(1+r)^x`

where:

• a = initial amount
• r = rate of growth (in decimal form)
• x = time (in years)

Given:

• a = 500
• r = 0.06

`\implies f(x)=500(1+0.06)^x`

`\implies f(x)=500(1.06)^x`

Part (e)

when x = 3

`\begin{aligned}\implies f(3) & =500(1.06)^3\\ & = 595.51\: \sf(nearest\:hundredth)\end{aligned}`