The current student population of New York City is 1400. If the population decreases at a rate of 9.1% each year. What will the student population be in 9 years? Write an exponential growth model for the future population P(x) where x is in years
Given that the student population decreases at a rate of 9.1% each year, we can write the exponential growth model as:
P(x) = P(0) * (1 - r)^x
Where:
P(0) is the initial population (1400),
r is the growth rate (-0.091),
x is the number of years.
Substituting the values into the model:
P(x) = 1400 * (1 - (-0.091))^9
Simplifying the expression within the parentheses:
P(x) = 1400 * (1.091)^9
Calculating the exponent:
P(x) = 1400 * 1.99962
Rounding the result to the nearest whole number, the student population in 9 years will be 2800.