Question

Which exponential function goes through the points (3, 48) and (6, 384)?

A) f(x) = 384(6)x
B) f(x) = 2(6)x
C) f(x) = 48(3)x
D) f(x) = 6(2)x

Answer 1

The exponential function that goes through the points (3, 48) and (6, 384) is f(x) = 48(3)^x.

Step-by-step explanation:

The exponential function that goes through the points (3, 48) and (6, 384) is f(x) = 48(3)^x.

To find the exponential function, we need to use the formula f(x) = ab^x, where a is the initial value and b is the growth factor. Plug in the values of the two points to get two equations:

1) 48 = a(3)^3

2) 384 = a(3)^6

Solving the first equation, we get a = 16. Substituting this value in the second equation, we find that b = 2. Hence, the exponential function is f(x) = 48(3)^x.