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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?

Respuesta :

luisongonz

Answer:

[tex]P(t)=80(10^{0.1t})[/tex]

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:

[tex]log(P)=0.1t+C[/tex]

Pow each part of the equation by 10:

[tex]10^{log(P)}=10^{0.1t+C}\\ P=10^{0.1t+C}[/tex]

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

[tex]P(0)=10^{C}=80[/tex]

Applying logarithmic properties:

[tex]P=10^{0.1t+C}=10^{0.1t}*10^{C}[/tex]

So, the final function is:

[tex]P(t)=80(10^{0.1t})[/tex]

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