Question

Can someone explain this to me? Which exponential function goes through the points (1, 32) and (4, 2048)?

Answer 1

Let y = a * b^x be the exponential function.
when x = 1, y = 32: 32 = a * b^1 or ab = 32 ---- (1)
when x = 4, y = 2048: 2048 = a * b^4 or ab^4 = 2048 ---- (2)

Divide (2) / (1): b^3 = 2048/32 = 64
b = 4
put it in (1):
a * 4 = 32
a = 8

y = 8 * (4)^x