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

Answer:

$P(t)=80(10^{0.1t})$

Step-by-step 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:

$P(t)=80(10^{0.1t})$