Question

Write an exponential function in the form y=abˣ hat satisfies the points (0, 16) and (3, 2000).

Answer 1

To find the exponential function y=ab^x that passes through the points (0, 16) and (3, 2000), we use the first point to find a = 16 and use the second point to solve for b, which is b = 5. The resulting function is y = 16∙5^x.

Step-by-step explanation:

To write an exponential function in the form y = abx that satisfies the points (0, 16) and (3, 2000), we can use the given points to find the values of a and b.

1. Using the point (0, 16), we can determine a directly because any number raised to the zero power is one. So, a = 16.
2. Now, using the point (3, 2000) with a known, we can find b. Substituting into the equation, we get 2000 = 16 ∙ b3. Solving for b gives us b = ∙{(2000/16)}1/3, which simplifies to b = 5.

So, the exponential function is y = 16 ∙ 5x.