Question

Write an exponential function in the form y = ab* that goes through the points (0, 13) and

(3,6656).
Answer Attempt 2 out of 2
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Answer 1

To find the exponential function in the form y = ab^x that goes through the points (0, 13) and (3, 6656), we can use the given points to form a system of equations.

Using the point (0, 13), we have:
13 = ab^0
13 = a

Using the point (3, 6656), we have:
6656 = ab^3

Substituting the value of a from the first equation into the second equation:
6656 = 13 * b^3
Dividing both sides of the equation by 13:
512 = b^3

Taking the cube root of both sides, we find:
b = 8

Now that we have the value of b, we can substitute it back into the first equation to find a:
13 = a * 8^0
13 = a * 1
13 = a

So the exponential function in the form y = ab^x that goes through the points (0, 13) and (3, 6656) is:
y = 13 * 8^x