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?

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?

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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}(e^{n}) = 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 !