5. A mouse population is 25,000 and is decreasing at a rate of 20% per year. Write anexponential function to model the situation. Enter your answer in the form y = a(b)^x

Respuesta :

Solution:

Given:

Using the population decrease formula,

[tex]\begin{gathered} y=ab^x \\ where:b=1-r.....................(decreasing\text{ population\rparen} \\ \\ Hence, \\ y=a(1-r)^x \end{gathered}[/tex]

where:

[tex]\begin{gathered} a=25000 \\ r=\frac{20}{100}=0.2 \\ y=a(1-r)^x \\ y=25000(1-0.2)^x \\ y=25000(0.8)^x \end{gathered}[/tex]

Therefore, the exponential function is;

[tex]y=25000(0.8)^x[/tex]

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