how do you solve for time(t) using the pe^rt equation

Question

Exponential growth

A=pe^kt

A biologist is studying new bacteria. She places 250 bacteria in a petri-dish, that has a growth of 10.5, how many hours will it take for the bacteria to reach 2,000?

Answer 1

Hello Miranda,

A=pe^kt

=> ln(A) = ln(pe^kt)           'ln' is natural logarithm, logarithm function to the base 'e' [log_e]

              = ln(p) + ln(e^kt)     log (xy) = log(x) + log(y)

              = ln(p) + kt                log_e(eⁿ) = n log_e(e) ; log_e(e) = 1

=> t = [ln(A) - ln(P)]/k

Now you are given values of P, A and k. Plug them in to get t. 

Note: Look into the units of your problem. You are asked to find time in hours. The units of your answer depend on the units of 'k'. If k has different time units, convert your answer to hours.

Good Luck !