Question

a population of 240 birds increases at a rate of 16% annually. jemel writes an exponential function of the form f(x)=ab^x to represent the number of birds after x years. which values should she use for a and b?

Answer 1

Explanation:

To find the values of a and b in the exponential function, we need to use the given information about the population growth rate.

The formula for exponential growth is:

f(x) = a * (1 + r)^x

where:

a = initial value

r = growth rate

x = time

In this case, we know that the initial population is 240 birds and the growth rate is 16% per year. We can convert the percentage to a decimal by dividing by 100:

r = 16% / 100 = 0.16

Now we can plug in the values we have:

f(x) = a * (1 + r)^x

f(x) = 240 * (1 + 0.16)^x

Simplifying:

f(x) = 240 * 1.16^x

So the values for a and b are:

a = 240

b = 1.16

Answer 2

To find the values of a and b, we need to use the given information about the population and the growth rate.

At the start (x=0), the population is 240 birds. This means that f(0) = 240, which gives us the value of a in the function:

f(0) = ab^0 = a = 240

Next, we need to find the value of b. We know that the population increases at a rate of 16% annually, which means that it grows by a factor of 1.16 each year. In other words, b = 1.16.

Therefore, the exponential function that represents the number of birds after x years is:

f(x) = 240(1.16)^x

Note that the value of b is greater than 1, which means that the function represents exponential growth.