Interpret the following exponential function: y = 6 (1.07) ^x What is the growth/decay factor? What is the y-interce

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

0

Answers ( No )

    0
    2021-10-04T11:22:24+00:00

    i believe the answer is d but i might be wrong

    0
    2021-10-04T11:22:27+00:00

    Answer:

    option d is correct.

    Growth factor is 1.07;

    y-intercept is 6

    Step-by-step 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

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