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8-36.
  1. The graph of an exponential function y = abx + k passes through (3, 7.5) and (4, 6.25). It also has an asymptote at y = 5. Homework Help ✎

    1. What is the equation of the function?

    2. If the function also passes through (8, w), what is the value of w?

Substitute 5 for k and then use the points to write a system of equations.

Rewrite each equation by subtracting 5 from both sides.

Solve the first equation for a.

Substitute for a in the second equation.

Solve for b.

Substitute 1/2 for b to solve for a.

k = 5
7.5 = ab3 + 5
6.25 = ab4 + 5

ab3 = 2.5
ab4 = 1.25

a = 20

Substitute 8 for x and w for y.