Question

Exponential growth/decay problem 2

Answer 1

a) decay

b) 2,950,000

c) 0.025

d)
`f(x)=2950000(0.975)^x`

e) 2,409,123

Explanation:

Part (a)

Exponential DECAY, since the population was decreasing annually.

Part (b)

Initial amount = 2,950,000 people (in the year 2000)

Part (c)

Decay factor = 2.5% = 0.025 (in decimal form)

Part (d)

General form of exponential decay function:

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

where:

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

Given:

• a = 2950000
• r = 0.025

`\implies f(x)=2950000(1-0.025)^x`

`\implies f(x)=2950000(0.975)^x`

Part (e)

To determine the city's population in 2008:

`x = 2008 - 2000 = 8`

`\begin{aligned}\implies f(8) & =2950000(0.975)^8\\ & = 2409123\: \sf(nearest\:whole\:number)\end{aligned}`