Question

Find a value a>0 so that the graph of the exponential function f(x)=aˣ contains the point (2,1/16).

(A) a=1/4
(B) a=4
(C) a=−1/4
(D) a=−4

Answer 1

To find the value of a that makes the graph of the exponential function f(x) = aˣ contain the point (2, 1/16), substitute the values into the equation and solve for a. The correct value of a is 1/4.

Step-by-step explanation:

To find the value of a that makes the graph of the exponential function f(x) = aˣ contain the point (2, 1/16), we can substitute the values of x and f(x) into the equation and then solve for a.

Substitute x = 2 and f(x) = 1/16 into the equation:
1/16 = a²

Solve for a by taking the square root of both sides:
a = ±√(1/16) = ±1/4

Therefore, there are two possible values for a: a = 1/4 and a = -1/4. However, since the question specifies that a > 0, the correct value of a is a = 1/4.