Answer:
a) decay
b) 2,950,000
c) 0.025
d) [tex]f(x)=2950000(0.975)^x[/tex]
e) 2,409,123
Step-by-step 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:
[tex]f(x)=a(1-r)^x[/tex]
where:
- a = initial amount
- r = rate of decay (in decimal form)
- x = time (in years)
Given:
[tex]\implies f(x)=2950000(1-0.025)^x[/tex]
[tex]\implies f(x)=2950000(0.975)^x[/tex]
Part (e)
To determine the city's population in 2008:
[tex]x = 2008 - 2000 = 8[/tex]
[tex]\begin{aligned}\implies f(8) & =2950000(0.975)^8\\ & = 2409123\: \sf(nearest\:whole\:number)\end{aligned}[/tex]
