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mr Goodwill [35]
3 years ago
13

Find an exponential function that passes through each pair of points.(2,1.75) & (-2,28)

Mathematics
1 answer:
dusya [7]3 years ago
8 0

Answer:

f(x) = 7\, ((1/2)^{x}).

Step-by-step explanation:

An exponential function is typically in the form f(x) = a\, (b^{x}), where a and b (b > 0) are constants to be found.

In this question:

f(2) = 1.75 means that a\, (b^{2}) = 1.75.

f(-2) = 28 means that a\, (b^{-2}) = 28.

Divide one of the two equations by the other to eliminate a and solve for b.

The number of the right-hand side of the second equation is larger than that of the first equation. Hence, divide the second equation with the first:

\displaystyle \frac{a\, (b^{-2})}{a\, (b^{2})} = \frac{28}{1.75}.

\displaystyle b^{-4} = 16.

b^{-1} = 2.

\displaystyle b = \frac{1}{2}.

Substitute b = (1/2) back into either equation (for example, the first equation) and solve for a:

a\, ((1/2)^{2}) = 1.75.

a = 7.

Substitute a = 7 and b = (1/2) into the other equation. That equation should also be satisfied.

Therefore, this function would be:

f = 7\, ((1 / 2)^{x}).

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