The following function describes a certain population P(t)=Ce^ktwhere k is the c

Question

The following function describes a certain population P(t)=Ce^ktwhere k is the constant rate of growth and t is time measured inyears, (and I think C is the initial population). How do Ifind the value of k if the population is tripled in 23 years (thevalue of C was not provided in the question)? (I think I have totake the ln of both sides to isolate k, but I am totally lost onthis one...the other pre-calc questions I have answered like thishave provided the constants so plugging them into the equation waseasy.) Thanks to anyone who can help with any part of this question:-)! Heather
The following function describes a certain population P(t)=Ce^ktwhere k is the constant rate of growth and t is time measured inyears, (and I think C is the initial population). How do Ifind the value of k if the population is tripled in 23 years (thevalue of C was not provided in the question)? (I think I have totake the ln of both sides to isolate k, but I am totally lost onthis one...the other pre-calc questions I have answered like thishave provided the constants so plugging them into the equation waseasy.) Thanks to anyone who can help with any part of this question:-)! Heather

Explanation / Answer

Or you can think about it as dividing by C so you get P/Cwhich is the final pop / initial pop which we know is 3.
Anyway now we know C and P. They give us 23 years for t. Soall we have left is k. Use the natural log like use suggest andyou're good to go.

Anyway now we know C and P. They give us 23 years for t. Soall we have left is k. Use the natural log like use suggest andyou're good to go.

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