An initial population of 298 quail increases at an annual rate of 8%. Write an exponential function to model the quail population. What will the approximate population be after 3 years
f(x)=298(1.08)^x;375
f(x)=298(0.08)^x;153
f(x)=298(8)^x;305
f(x)=(298*1.08)^x;324
number = 298(1.08)^n , where n is the number of years
so when n = 3
population = 298(1.08)^3 = appr 375
Well, you've got a few options there. But I'm pretty sure the correct exponential function to model the quail population would be f(x) = 298(1.08)^x. So, let's see what the approximate population will be after 3 years.
Plug in x = 3 into the function: f(3) = 298(1.08)^3.
Calculating: f(3) ≈ 298(1.259712) ≈ 375.4.
So, the approximate population after 3 years will be around 375 quails. But beware, those quails might just be planning their next big party!
The correct exponential function to model the quail population is f(x) = 298(1.08)^x.
To find the approximate population after 3 years, we substitute x = 3 into the function:
f(3) = 298(1.08)^3
Simplifying this calculation:
f(3) ≈ 298(1.26)
f(3) ≈ 375.48
Therefore, the approximate population after 3 years is 375 quail.
To model the quail population, we can use the exponential growth formula:
f(x) = initial population * (1 + growth rate)^x
In this case, the initial population is 298 and the annual growth rate is 8%, which can be expressed as 0.08. So the correct exponential function to model the quail population is:
f(x) = 298 * (1.08)^x
Now, to find the approximate population after 3 years, we substitute x=3 into the function:
f(3) = 298 * (1.08)^3
Evaluating this expression gives us:
f(3) ≈ 324
Therefore, the approximate population after 3 years is 324.