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Write an exponential function that passes through the points (1, 12) and (5, 972)

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Answer:

Explanation:

An exponential function can be written in the form y = ab^x, where a is the initial value and b is the base. To find the specific exponential function that passes through the points (1, 12) and (5, 972), we need to solve for a and b.

Using the point (1, 12), we get:

12 = ab^1

12 = ab

Using the point (5, 972), we get:

972 = ab^5

We can use the equation ab from the first point to solve for a in terms of b:

a = 12/b

Substituting this expression for a into the second equation, we get:

972 = (12/b)b^5

Simplifying this equation, we get:

972 = 12b^4

Dividing both sides by 12, we get:

81 = b^4

Taking the fourth root of both sides, we get:

b = 3

Substituting this value of b into the equation a = 12/b, we get:

a = 4

Therefore, the exponential function that passes through the points (1, 12) and (5, 972) is:

y = 4(3^x)

User Ronan Fauglas
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