### Home > CCA2 > Chapter 7 > Lesson 7.2.3 > Problem 7-150

7-150.

An exponential function

*y*=*ab*+^{x }*k*passes through (3, 7.5) and (4, 6.25). It also has an asymptote at*y*= 5. Homework Help ✎Find the equation of the function.

If the equation 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*.

*k* = 5

7.5 = *ab*^{3} + 5

6.25 = *ab*^{4} + 5

*ab*^{3} = 2.5*ab*^{4} = 1.25

*a* = 20

Substitute 8 for *x* and *w* for *y*.