The current student population of Cincinnati is 2900. If the population increases at a rate of 9.4% each year. What will the student population be in 6 years. Write the exponential growth mode for the future population P[x] where x is in years.
To find the future population in 6 years, we can use the formula for exponential growth:
P[x] = P[0] * (1 + r)^x
where P[x] is the future population, P[0] is the current population, r is the growth rate (expressed as a decimal), and x is the number of years in the future.
In this case, the current population (P[0]) is 2900, and the growth rate (r) is 9.4% or 0.094 (expressed as a decimal). We want to find P[6], so x = 6.
Substituting these values into the formula:
P[6] = 2900 * (1 + 0.094)^6
Simplifying the equation:
P[6] = 2900 * (1.094)^6
Using a calculator to evaluate (1.094)^6:
P[6] ≈ 2900 * 1.6382
P[6] ≈ 4748.28
Therefore, the student population of Cincinnati in 6 years will be approximately 4,748.
To find the future student population in Cincinnati, you can use the exponential growth formula:
P[x] = P[0] * (1 + r)^x
Where:
P[x] is the future population after x years
P[0] is the initial population
r is the growth rate
x is the number of years
Given that the current student population (P[0]) is 2900 and the growth rate (r) is 9.4%, we can substitute these values into the formula:
P[x] = 2900 * (1 + 0.094)^x
Now we can write the exponential growth model for the future population of students in Cincinnati:
P[x] = 2900 * (1 + 0.094)^x