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A population numbers 10,000 organisms initially and decreases by 4.1% each year.
Suppose P represents population, and t the number of years of growth. An exponential model for the
population can be written in the form P = a b where
P=

A population numbers 10000 organisms initially and decreases by 41 each year Suppose P represents population and t the number of years of growth An exponential class=

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MrRoyal

Answer:

[tex]y = 10000 * 0.959^t[/tex]

Step-by-step explanation:

Given

[tex]a = 10000[/tex]

[tex]r = 4.1\%[/tex]

Required

Express as an exponential function [tex]y =ab^t[/tex]

First, we calculate the value of b;

Since the population decrease, then

[tex]b = 1 - r[/tex] --- This represents decrement of decay factor

Substitute [tex]r = 4.1\%[/tex]

[tex]b = 1- 4.1\%[/tex]

[tex]b = 0.959[/tex]

So:

[tex]y =ab^t[/tex] becomes

[tex]y = 10000 * 0.959^t[/tex]

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