Respuesta :
The equation for calculating the total population after t years [tex]f(t) = ae^r^t[/tex]
Given;
A city has a current population of 45,000 people and is losing 2% of its residents annually.
To get the formula for determining the total population after a period of t years;
⇒ [tex]f(t) = ae^r^t[/tex]
Here, a → Initial population
r → Rate of reduction
t → Time or period
As r is decreasing rate r = -0.02
Assume t = 4;
[tex]f(4) = 45000e^-^0^.^0^2^(^4^)[/tex]
[tex]f(4) = 45000*0.923\\ f(4) = 41535[/tex]
Hence, the formula for determining the total population after a period of t years is [tex]f(t) = ae^r^t[/tex].
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