Answer:
P = 178 (initial population size)
r = 32% = 0.32 (growth rate as a decimal)
n = 10 (number of years)
A = P(1 + r)^n
A = 178(1 + 0.32)^10
A = 178(1.32)^10
A ≈ 178(16.05976966)
A ≈ 2858.639
The expected population size after 10 years is approximately 2859.
Let's calculate the expected population size after 25 years with a 32% annual growth rate:
P = 178 (initial population size)
r = 32% = 0.32 (growth rate as a decimal)
n = 25 (number of years)
A = P(1 + r)^n
A = 178(1 + 0.32)^25
A = 178(1.32)^25
A ≈ 178(1033.589955)
A ≈ 183,979.0121
The expected population size after 25years is approximately 183,979.
To find out how long it will take for the population to reach 10,000, we need to solve for n:
P = 178
r = 32% = 0.32
A = 10,000
10,000 = 178(1 + 0.32)^n
Dividing both sides by 178:
5.592841163 = (1.32)^n
Taking the logarithm of both sides (base 10 or natural logarithm can be used):
log(5.592841163 ) = n * log(1.32)
Using logarithm properties, we can isolate n:
n = log(5.592841163 ) / log(1.32)
n ≈ 6.200614661
So, it will take approximately 6.20 years for the population to reach 10,000.