Question

What is the growth/decay factor? What is the y-intercept?
Y=6(1.07)^x

Answer 1

y intercept is when x=0
y= 6*1.07^0 = 6*1 = 6

growth/decay factor is usually the base of the exponential term or 1.07

Answer 2

An exponential function is given by:

`y = ab^x` .....[1]

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.

Given the function:

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

On comparing with [1] we have;

a=6 and b = 1.07

Since, b = 1.07 > 1

Therefore, this is exponentially growth function.

⇒the growth factor(b) = 1.07

Now, find the y-intercept.

y-intercept states that the line crosses the y-axis.

Substitute x = 0 and solve for y;

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

`y=6`

y-intercept = (0, 6)

Therefore, the growth factor(b) = 1.07 and y-intercept = (0, 6)