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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?

Verified Answer :

HomertheGenius

An exponential function is :
f ( x ) = a b^x,
where x is the number of the years.
a = 240   ( number of the birds at start )
16 % = 0.16
b = 1 + 0.16 = 1.16
f ( x ) = 240 1.16^x
Answer:
a = 240,   b = 1.16

Answer:

Hence the values of a and b are given by:

a=240

and b=1.16.

Step-by-step explanation:

It is given that:

A population of 240 birds increases at a rate of 16% annually.

i.e. the initial population of birds is 240.

Also they are increasing at a rate of 16% =0.16.

Hence, it clearly implies that the growth is exponential and the function that represents the population of the birds after x years is given by:

\(f(x)=240\times (1+0.16)^x\\\\\\f(x)=240\times (1.16)^x\)

Hence, on comparing our function with the exponential function:

\(f(x)=ab^x\)

we have:

a=240

and b=1.16.

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