Question

HELP ASAP PLEASE!!!

Give the equation: y=50(1.15)^x

A. Does this equation represent exponential growth or decay

B. What is the initial value?

C. What is the rate of growth or decay?

Answers

A. growth, 50, 15%

B. decay, 115, 50%

C. growth, 1.15, 0.15%

Answer 1

Option C is correct.

Explanation:

An exponential function is of the form:
`y =a(b)^x` ....[1] where a is the initial value, x is any real number and b is the growth factor

Also, the b value (growth factor) has been replaced either by (1 + r) or by (1 - r).

Then, the growth "rate" (r) is determined as b = 1 + r.

and the decay "rate" (r) is determined as b = 1 - r

• If b> 1, then it is exponential growth function.

• if 0<b< 1. then it is exponential decay function.

Also, b = 1+ 4

Given the equation:
`y = 50(1.15)^x`

On comparing given equation with [1] we get;

a = 50 and b = 1.15

Since, b = 1.15 > 1

Therefore, the given equation represents the exponential growth.

(A)

Yes, this
`y = 50(1.15)^x` equation represents the exponential growth.

(B)

Initial value (a) = 50

(C)

Here growth factor, b = 1.15

and

1+ r = 1.15.

⇒
`r = 0.15\%`