Answer:
Step-by-step explanation:
The formula for calculating exponential growth is expressed as
A = P(1 + r)^t
where
A is the population after a period of t months
P is the initial population
r is the growth rate
t is the time
From the information given
P = 150
r = 15% = 15/100 = 0.15
t = 12 because there are 12 months in a year
Thus, the exponential growth after 1 year is
A = 150(1 + 0.15)^12
A = 150(1.15)^12
A = 802.5375
Rounding to the nearest whole number,
A = 803
After 1 year, the growth is linear with a slope of 150 individuals per month. The linear equation would be
A = 150t + 803
where
t is the number of months
Since there are 12 months in a year, we would find the size of the population 2 years after the beginning of the growth model by substituting t = 12 into the linear function. We have
A = 150 * 12 + 803
A = 2603
The size of the population 2 years after the beginning of the growth model is 2603