Approximating the Solution of an Exponential Equation

Solve $42 = 1.2 {(5)}^{x} + 2.8$ graphically. Round to the nearest thousandth.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Press [Y=] and enter $1.2 {(5)}^{x} + 2.8$ next to Y₁=. Then enter 42 next to Y2=. For a window, use the values –3 to 3 for $x$ and –5 to 55 for $y .$ Press [GRAPH]. The graphs should intersect somewhere near $x = 2.$

For a better approximation, press [2ND] then [CALC]. Select [5: intersect] and press [ENTER] three times. The x-coordinate of the point of intersection is displayed as 2.1661943. (Your answer may be different if you use a different window or use a different value for Guess?) To the nearest thousandth, $x \approx 2.166.$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve $4 = 7.85 {(1.15)}^{x} - 2.27$ graphically. Round to the nearest thousandth.

How did it go?