### Home > PC > Chapter 4 > Lesson 4.2.4 > Problem 4-118

4-118.

An exponential function passes through the points (1, 70) and (3, 145). The function has a horizontal asymptote at *y* = 10. Find an equation for the function. Homework Help ✎

Write the general equation for this problem.

Substitute the points in for (*x*, *y*), creating two equations and two unknowns.

Subtract 10 on both sides.

Then divide one equation by the other.

Substitute the *b*-value back into one of the original equations and solve for *a*. Then substitute *a* and *b* into the general equation.

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

145 = *a*(*b*^{3}) + 10

70 = *a*(*b*^{1}) + 10

135 = *a*(*b*^{3})

60 = *a*(*b*^{1})

2.25 = *b*^{2}*b* = 1.5