### Home > CC4 > Chapter 11 > Lesson 11.2.1 > Problem 11-49

11-49.

Write the equation of an exponential function that passes through each pair of points. Homework Help ✎

a.

(1, 7.5) and (3, 16.875)

b.

(−1, 1.25) and (3, 0.032)

To start, write a system of equations in the form *y* =*ab ^{x}* by substituting the points in for

*x*and

*y*.

16.875 = *ab*^{3}

7.5 = *ab*^{1}

Divide the 2nd equation into the first to eliminate *a*.

2.25 = *b*^{2}

Solve for *b*.

Substitute the *b* value you found into one of the original equations.

Solve for *a*.

Substitute both *a* and *b* back into the original equation with along with *x* and *y*.

*y* = 5(1.5)^{x}

*y* = 0.5(0.4)^{x}