The number of students at a university is 1320, and the number increases by 8% each year. Write an exponential function to model this situation. Then find about how many students there will be in 5 years.

P = Po(1+r)^t

P = 1320(1.08)^5 = 1940 Students.

Thank you

To model the situation described, we can use the exponential growth function:

P(t) = P₀ * (1 + r)^t

where:
P(t) is the population at time t
P₀ is the initial population
r is the growth rate (expressed as a decimal)
t is the time period

Given that the initial number of students is 1320 and the number increases by 8% each year, we can set up the function as:

P(t) = 1320 * (1 + 0.08)^t

To find the number of students in 5 years, we substitute t = 5 into the function:

P(5) = 1320 * (1 + 0.08)^5

Now we can calculate P(5) using a calculator or by hand:

P(5) = 1320 * (1.08)^5

P(5) ≈ 1320 * 1.469329

P(5) ≈ 1937.3

So, in approximately 5 years, there will be about 1937 students at the university.

To model the situation, we can use the formula for exponential growth:

A = P(1 + r)^t

Where:
A represents the final amount,
P represents the initial amount,
r represents the growth rate as a decimal, and
t represents the number of time periods.

In this case, the initial amount (P) is 1320, the growth rate (r) is 8% or 0.08 as a decimal, and the number of time periods (t) is 5 years.

So the exponential function to model this situation is:

A = 1320(1 + 0.08)^5

Now, let's calculate the final amount by plugging in the values:

A = 1320(1.08)^5
A = 1320(1.46933)
A ≈ 1937.875

Therefore, there will be approximately 1,937 students in 5 years.