A population of 240 birds increases at a rate of 16% annually. Jemel writes an exponential function of the form f(x) =abx to represent the number of birds after x years. Which values should she use for a and b?
You must have meant:
f(x) = a b^x
In this case, a = 240
b = 1.16
so f(x) = 240(1.16)^x
To find the values of "a" and "b" in the exponential function f(x) = ab^x, we need to use the given information about the population growth rate.
The population increases at a rate of 16% annually, which means that the population will grow by a factor of 1.16 (100% + 16%) each year.
Let's use the given initial population of 240 birds as a baseline.
Now, we can set up the equation f(x) = ab^x, with "a" representing the initial population of 240 birds:
f(x) = 240 * b^x
To find the value of "b," we need to use the growth rate. Since the population grows by a factor of 1.16 each year, we can set up the equation:
1.16 = b^1
Simplifying, we have:
b = 1.16
Thus, the values for "a" and "b" in the exponential function f(x) = ab^x are:
a = 240
b = 1.16
To find the values of "a" and "b" in the exponential function, we need to use the given information.
Since the population increases at a rate of 16% annually, the growth factor, "b," will be calculated by adding 1 (representing 100%) to the growth rate expressed as a decimal:
b = 1 + growth rate in decimal form
= 1 + 0.16
= 1.16
Now, we need to determine the initial population, which would be the value of "f(0)" in the function. We are given that the initial population is 240 birds.
So, we have the equation f(0) = a * b^0 = a * 1, where f(0) = 240.
Therefore, a = 240.
Hence, the values of "a" and "b" in the exponential function would be a = 240 and b = 1.16.
Thus, the function representing the number of birds after x years is f(x) = 240 * 1.16^x.