Question

Which exponential function goes through the points (1, 8) and (4, 64)? f(x) = 4(2)x f(x) = 2(4)x f(x) = 4(2)−x f(x) = 2(4)−x

Answer 1

Answer:

y = 4(2^x)

Step-by-step explanation:

To write the exponential values, compare the y values. Notice they are multiples of 8 and they are increasing. This means the base is likely 2 or 4 since each of these numbers has the same multiples. Our options also only include base 2 and 4.

Try 4^1 = 4 and 4^4 = 256.

Try 2^1 = 2 and 2^4 = 16.

None of these give the exact values in the points. This means there is an initial value multiplied to them as well.

When x = 1 and the base is 4, the value is too small. But when x = 4, the value is too large. This cannot be reconciled.

When x = 1 and x = 4 for the base 2, both values are too small and could be multiplied by the same number to get the right values.

2*4 = 8

16*4 = 64

The initial value is 4 so the function is $y = 4(2^x)$