Question

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?

Answer 1

Answer:

$\boxed{\boxed{a = 240, b = 1.16}}$

Step-by-step explanation:

General exponential function for growth or decay is,

$y=a(1\pm r)^{x}$

Where,

a = initial value,

r = rate of change

+ is used for growth and - is used for decay.

As here, the number of birds increasing so, the exponential function is,

$y=a(1+r)^{x}$

And initial value a = 240, r = rate of change = 16% = 0.16

Putting the values,

$y=240(1+0.16)^{x}\\\\y=240(1.16)^{x}$

Comparing this with the given equation $y=ab^{x}$

Hence, a = 240, b = 1.16

Answer 2

Answer:

The value of a is 240 and b is 1.16.

Step-by-step explanation:

Given,

The initial population of the birds = 240,

Annual rate of increasing = 16 %,

Hence, the population of birds after x years

$P=240(1+\frac{16}{100})^x$

$=240(1+0.16)^x$

$=240(1.16)^x$

We can put P = f(x), ( because, f(x) also shows the population of birds after x years )

$\implies f(x) = 240(1.16)^x$ --------(1)

According to the question,

$f(x) =ab^x$ --------(2),

From equation (1) and (2),

a = 240 and b = 1.16