121k views
4 votes
For the exponential equation
y = 3.4(0.66)^x is it a growth or decay function and what is the y-intercept and the rate of growth or decay?

A) Growth, y- intercept = 1, rate is 66%

B) Decay, y- intercept = 3.4, rate is 34%

C) Decay, y- intercept = 3.4, rate is 66%

D) Growth, y- intercept = 3.4, rate is 34%

User Jou
by
8.0k points

1 Answer

5 votes

Answer:

Option: B is the correct answer.

B) Decay, y- intercept = 3.4, rate is 34%

Explanation:

We are given an exponential equation as follows:


y=3.4(0.66)^x

We know that any exponential function of the type:


y=ab^x

is growth function if: b>1

and is a decay function if 0< b< 1

Hence, here we have: b=0.66<1

Hence, the function is a decay function.

Also, we know that the y-intercept of a function is the point where x=0

Hence, we take x=0

we have:
y=3.4* (0.66)^0\\\\\\y=3.4

Hence, the y-intercept is: 3.4

Also, the rate of a function is denoted by 'r'

where b=1-r

⇒ 0.66=1-r

⇒ r=1-0.66

⇒ r=0.34

Hence, the rate is: 34%

option: B is the correct answer.

User Helam
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories