The function h is defined by h(x) = a^x + b, where a and b are positive constants. The graph of y = h(x) passes through (0, 10) and (-2, 325/36). What is the value of ab?
A1/4
B1/2
C54
D60
Answer & Solution
Correct answer: C. 54
h(0) = 1 + b = 10, so b = 9. h(-2) = a^(-2) + 9 = 325/36, so a^(-2) = 1/36, meaning a^2 = 36, a = 6 (positive). ab = 6 * 9 = 54.
Related questions
Alma bought a laptop computer at a store that gave a 20 percent discount off its original Which of the following numbers is NOT a solution of the inequality 3x - 5 >= 4x - 3?Using a = 1052 + 1.08*t, at which of the following air temperatures will the speed of a soThe speed of a sound wave in air depends on the air temperature. The formula above (a = 10If y = kx where k is a constant, and y = 24 when x = 6, what is the value of y when x = 5?If (ax + 2)(bx + 7) = 15x^2 + cx + 14 for all x, and a + b = 8, what are the two possible If x > 3, which is equivalent to 1 / (1/(x + 2) + 1/(x + 3))?A line in the xy-plane passes through the origin and has slope 1/7. Which point lies on th