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Elis [28]
3 years ago
14

The graph of an exponential function has a y-intercept of 8 and contains the point (3,64). Find the exponential function that de

scribes the graph.
Mathematics
2 answers:
Brums [2.3K]3 years ago
6 0

Given:

Y-intercept of exponential function is 8.

It contains the point (3,64).

To find:

The exponential function that describes the graph.

Solution:

The general form of an exponential function is

y=ab^x      ...(i)

where, a is initial value or y-intercept and b is growth factor.

Since, y-intercept is 8, therefore, a=8.

Put a=8 in (i).

y=8b^x         ...(ii)

It contains the point (3,64). Put x=3 and y=64.

64=8b^3

Divide both sides by 8.

\dfrac{64}{8}=b^3

8=b^3

2^3=b^3

On comparing both sides, we get

b=2

Put b=2 in (ii).

y=8(2)^x

The functions form of this equation is

f(x)=8(2)^x

Therefore, the required function is f(x)=8(2)^x.

QveST [7]3 years ago
5 0

Answer: Do you have a picture

Step-by-step explanation:

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