Question

Suppose that you follow a population over time. When you plot your data on a semilog plot (using logs with base 10), a straight line with slope 0.1 results. Furthermore, assume that the population size at time 0 was 80. What function best describes the population size at time t?

Answer 1

`P(t)=80(10^(0.1t))`

Explanation:

The 'y' axis represent log(P), so it may be modeled as a line (or linear function), where its slope is 0.1:

`log(P)=0.1t+C`

Pow each part of the equation by 10:

`10^(log(P))=10^(0.1t+C)\\ P=10^(0.1t+C)`

Evaluate at t=0, where the population is known.

`P(0)=10^(C)=80`

Applying logarithmic properties:

`P=10^(0.1t+C)=10^(0.1t)*10^(C)`

So, the final function is:

`P(t)=80(10^(0.1t))`