Question

For the exponential equation )^x" alt="y = 3.4(0.66)^x" align="absmiddle" class="latex-formula"> 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%

Answer 1

Answer:

Option: B is the correct answer.      

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

Step-by-step 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:  $y=3.4\times (0.66)^0\\\\\\y=3.4$

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.