Question

Interpret the following exponential function:

y = 6 (1.07) ^x

What is the growth/decay factor? What is the y-intercept?
a.
Decay factor is 6; y-intercept is 1.07
b.
Decay factor is 1.07; y-intercept is 6
c.
Growth factor is 6; y-intercept is 1.07
d.
Growth factor is 1.07; y-intercept is 6

Answer 1

i believe the answer is d but i might be wrong

Answer 2

option d is correct.

Growth factor is 1.07;

y-intercept is 6

Explanation:

An exponential function is given by:

`y = ab^x`

where, a is the initial amount.

If b > 1, then this is exponentially growth function.

If 0<b<1, then this is exponentially decay function.

As per the statement:

The exponential function is:

`y = 6 \cdot (1.07)^x`

On comparing with [1] we have;

Since, b = 1.07 > 1

this is a exponential growth function.

⇒the growth factor = 1.07

Now: find y-intercept:

y-intercept:

Substitute x = 0 ans solve for y:

then;

`y = 6 \cdot (1.07)^0`

⇒
`y = 6 \cdot 1`

Simplify:

`y = 6`

therefore, the Growth factor is 1.07 and the y-intercept is 6