Based on census data, the population of Freedonia is modeled by the function P(t)= 310t^2+25474 people, where t represents the number of years after 1990. Use this function to determine how fast the population was increasing at the end of the year 1995.
not quite.
t = 5
1995 is 5 years after 1990
To determine how fast the population was increasing at the end of the year 1995, we need to find the derivative of the population function with respect to time, and then evaluate it at t=5 (since 1995 is 5 years after 1990).
The population function is given by:
P(t) = 310t^2 + 25474
To find the derivative, we differentiate the function with respect to t:
P'(t) = d/dt (310t^2 + 25474)
Using the power rule for differentiation, we get:
P'(t) = 620t
Now we can evaluate the derivative at t=5 to find the rate of population growth at the end of 1995. Substitute t=5 into the derivative equation:
P'(5) = 620(5)
P'(5) = 3100
Therefore, the population was increasing at a rate of 3100 people per year at the end of 1995.
Substitute t for 1995 in the function:
P(t) = 310*1995^2+25474