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Construct the exponential function that contains the points (0,−5) and (4,−80)

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raphealnwobi

The exponential function that contains the points (0,−5) and (4,−80) is:

y = -5(2ˣ)

An exponential function is given by:

y = a(bˣ)

where y, x are variables, a is the value of y when x is 0, and b is a constant.

Given the points  (0,−5) and (4,−80):

We can deduce that a = -5, since when x = 0, y = -5. The equation becomes:

y = -5(bˣ)

At point  (4,−80):

-80 = -5(b⁴)

16 = b⁴

[tex]b=\sqrt[4]{16} \\\\b=2[/tex]

Hence the exponential function is: y = -5(2ˣ)

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