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

Exponential growth


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?

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1 Answer

Hello Miranda,


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

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

              = ln(p) + kt                loge(en) = n loge(e) ; loge(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 !