Question

Which function represents exponential growth

y= 14(0.95)^x
y= 14x^1.95
y= 14(1.95)^x
y= 14/(1.95^x)

Answer 1

Option 3 -
`y=14(1.95)^x`

Explanation:

To find : Which function represents exponential growth?

Solution :

The general form of exponential function is
`f(x)=a(b)^x`

where, a is the initial value and b is the growth/decay rate factor.

If b>1 then it is the growth factor.

If b<1 then it is decay factor.

Now, From the given options

1)
`y=14(0.95)^x`

Since, 0.95 <1 it is a decay exponential function.

2)
`y=14x^(1.95)`

It is not in form of exponential function.

3)
`y=14(1.95)^x`

Since, 1.95 >1 it is a growth exponential function.

4)
`y=14/(1.95)^x`

It is not in form of exponential function.

Therefore, Option 3 is correct.

Answer 2

The exponential function with a base greater than 1 is

14(1.95)^x