Multiple choice an initial population of 293 quail increases at an annual rate of 6%. write an exponential function to model the quail population. what will the approximate population be after 4 years

Equation: 293(1.06)^4     Quail in 4 years: 369.9 which is about 370

Step-by-step explanation:

For exponential growth, the equation used is y=a(1+r)^t where a is the initial amount, r is the growth rate, and t is time. The equation can also be written as y=a(1+r)^x

Finding a

a value is the initial amount. In this case, we are starting with 293 quail so our a value is 293

Finding r

The population is increasing at an annual rate of 6%. This is the same as .06. To change percentage to decimal, move the decimal over to the left two spaces.

Finding t

t is also known as x. It is usually time. We are looking for the new number of quail in 4 years, so the value of t will be 4.

Putting it all together

If we plug in all of our values to y=a(1+r)^x we should get y=293(1+.06)^4. Finish combining to get a final equation of y=293(1.06)^4. Type this into your calculator, google calculator, or do it by hand and you should get 369.9057493, or 370 quail.

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