Answer:
a.
b. Population after 3 years is 142
c. 50 years
Step-by-step explanation:
Given
Type of growth: Exponential
Initial number of rats = 120
Number of rats (15months) = 280
Solving (a)
Since the growth type is exponential, we make use of the following exponential progression
Where Xo is the initial population;
Xo = 125
is the current population at T month
So;
; when
Substitute these values in the above formula
Divide both sides by 120
Take 15th root of both sides
Subtract 1 from both sides
(Approximated)
Plug in values of R and Xo in
Write as a function
Hence, the function is
Solving (b):
Population after 3 years
In this case, T = 3
So:
(Approximated)
Solving (c): When population will reach 2000
Here: X(T) = 2000
So:
So:
Divide both sides by 120
Take Log of both sides
Apply law of logarithm
Divide both sides by Log(1.058)
Approximate