Math logarithms

Question

The population, P, of prairie dogs increases according to the equation P= 2250e^r•t, where t is the number of years, and r is the rate of growth. Write the equation for r?

Answer 1

For this question, you need to isolate r on one side of the equation. When you are given an equation and asked for the equation for another variable, what you are really being asked to do is solve for it.

P = 2250e^rt (divide both sides by 2250)

P/2250 = e^rt (then take the natural log)

ln(P/2250) = rt (finally, divide by t)

r = ln(P/2250)/t