Question

Decide whether the function is an exponential growth or exponential decay function, and find the constant percentage rate of growth or decay. (2 points)

f(x) = 5.9 ⋅ 1.01x

Answer 1

exponential growth because a number more than 1 has the exponent.the constant percentage rate of growth is 1%.

Answer 2

• The function is an exponential growth function .

• The growth percentage rate is: 1% .

Explanation:

We know that an exponential function is given by:

`f(x)=ab^x`

where a is the initial amount and b is called the base and x is called the exponent.

and if b>1 then the function is a growth function

and if 0<b<1 then the function is a decay function.

Here we have the function f(x) as:

`f(x)=5.9\cdot (1.01)^x`

Here b=1.01>1

Hence, the function is an exponential growth function.

Also,

the growth rate is: r

where 1+r=1.01

i.e. r=0.01

which in percent is: 1% ( Since 0.01×100=1% )