Answer:
(a) The population in 2000 is 450
(b) 15% decreases each year
Step-by-step explanation:
Given
[tex]P = 450(0.85)^t[/tex] --- since 2000
[tex]P \to Population[/tex]
[tex]t \to years[/tex]
Solving (a): The population in 2000
First calculate t
[tex]t = 2000 - 2000[/tex] --- years since 200
[tex]t = 0[/tex]
So, we have:
[tex]P = 450(0.85)^t[/tex]
[tex]P = 450 * 0.85^0[/tex]
[tex]P = 450 * 1[/tex]
[tex]P = 450[/tex]
Solving (b): Rate of population decrease
A function that decreases is represented as:
[tex]P(t) = a(1 - r)^t[/tex]
Where
[tex]r \to[/tex] rate of decrement
Compare [tex]P(t) = a(1 - r)^t[/tex] and [tex]P = 450(0.85)^t[/tex]
[tex]1- r = 0.85[/tex]
Collect like terms
[tex]r = 1 - 0.85[/tex]
[tex]r = 0.15[/tex]
Express as percentage
[tex]r = 15\%[/tex]
