As indicated in the figure, the graph of y aebx passes

Chapter 5, Problem 68

(choose chapter or problem)

As indicated in the figure, the graph of y aebx passes through the two points (2, 10) and (8, 80). Follow steps (a) through (c) to determine the values of the constants a and b. y x (2, 10) (8, 80) y=ae bx 0.1 x 0.1 y 0.4 0.4 y=x y=ln(1+x) 1 p ln log10 A log10 B log10 C log101ABC2 (a) Since the point (8, 80) lies on the graph, the pair of values x 8 and y 80 satisfies the equation y aebx; that is, (1) Similarly, since the point (2, 10) lies on the graph, we have (2) Now use equations (1) and (2) to show that b (ln 8)/6. (b) In equation (2), substitute for b using the expression obtained in part (a). Show that the resulting equation can be written 10 a(eln 8) 1/3. (c) Use one of the properties of logarithms to simplify the right-hand side of the equation in part (b), then solve for a. (You should obtain a 5.) In Exe