An initial population of 620 birds increases at an annual rate of 16% write an exponential function to model the bird population what will the approximate population be after four years?

Answer :

approximate

[tex]y=620(1.16)^x\rightarrow\text{ model}[/tex]

after 4 years: 1123 birds

Explanation

o calculate exponential growth, use the formula:

[tex]\begin{gathered} y=a(1+b)^x \\ where\text{ a is the initial population} \\ b\text{ is the rate ( in decimal)} \\ x\text{ is the time ( in years)s} \\ y\text{ is the population after x years} \end{gathered}[/tex]

so

Step 1

Let

[tex]\begin{gathered} \text{ Initial value= a= 620} \\ \text{rate = 16 \%= }\frac{16\text{ }}{100}=0.16 \\ \text{time = 4 years} \end{gathered}[/tex]

now replace

[tex]\begin{gathered} y=a(1+b)^x \\ y=620(1+0.16)^3 \\ y=620(1+0.16)^x \\ y=620(1.16)^x\rightarrow\text{ model} \end{gathered}[/tex]

Step 2

now, evaluate for

x= 4 ( 4 years)

[tex]\begin{gathered} y=620(1.16)^x\rightarrow\text{ model} \\ y=620(1.16)^4 \\ y=620(1.8106) \\ y=1122.5964 \\ \text{rounded} \\ y=1123 \end{gathered}[/tex]

therefore

the aproxximate population after 4 years is 1123 birds

I hope this helps you

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