### Home > PC > Chapter 8 > Lesson 8.2.3 > Problem 8-109

8-109.

An exponential function has an asymptote at *y* = 10. The function passes through the points (4, 6) and (7, 8). Find the *y*-intercept for the function exactly and then calculate it to three decimal places. Homework Help ✎

Write the exponential form:

Substitute each point in for (*x*, *y*) forming two equations and two unknowns.

*y* = (*a*)*b ^{x}* + 10

6 = (*a*)(*b*)^{4} + 10

8 = (*a*)(*b*)^{7} + 10

Solve for '*a*' and '*b*' and substitute the contants into the function.

Using the new function, substitute '0' for '*x*' and simplify. This is the *y*-intercept.