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Charra [1.4K]
3 years ago
10

Help! I have looked at so many lessons on writing exponential functions from a graph and nothing has helped.

Mathematics
1 answer:
Over [174]3 years ago
4 0

Answer:

y = 8(-\frac{1}{2})^x

Step-by-step explanation:

Let the equation of the exponential function is,

y = a(b)ˣ

Since the graph of this function passes through two points (4, \frac{1}{2}) and (3, -1)

For the point (4, \frac{1}{2}),

\frac{1}{2}=a(b)^4 ---------(1)

For second point (3, -1),

-1 = a(b)³ ---------(2)

Divide equation (2) by equation (1),

\frac{\frac{1}{2}}{-1} = \frac{a(b)^4}{a(b)^3}

-\frac{1}{2}=b^{(4-3)}

-\frac{1}{2}=b

From equation (2)

-1 = a(-\frac{1}{2})^3

-1 = -\frac{1}{8}a

a = 8

Therefore, equation of the exponential function will be,

y = 8(-\frac{1}{2})^x

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