The population of the town of Missed Chances has, since January 1, 1972, been described by the function
P = 30000 ( 1.01 )^t
where P is the population t years after the start of 1972.
At what rate was the population changing on January 1, 1995? people per year
.0679
-358.4333
To find the rate at which the population was changing on January 1, 1995, we need to calculate the derivative of the population function with respect to time.
The given population function is: P = 30000(1.01)^t
To find the derivative, we can use the power rule of differentiation.
The power rule states that if we have a function of the form y = kx^n, where k and n are constants, then the derivative of this function with respect to x is given by: dy/dx = nkx^(n-1)
In our case, the function is P = 30000(1.01)^t, where k = 30000 and n = t.
Using the power rule, we can find the derivative of P with respect to t:
dP/dt = 30000 * ln(1.01) * (1.01)^(t-1)
Now, to find the rate at which the population was changing on January 1, 1995, we substitute t = 1995 - 1972 = 23 into the derivative:
dP/dt = 30000 * ln(1.01) * (1.01)^(23-1)
Calculating this expression will give us the rate at which the population was changing on January 1, 1995 in people per year.