Question

Write the function of the graph

Answer 1

y = 4[2]^x

Explanation:

One possible model for this function is the exponential y = a(b)^(kx). Notice that if x = 0, y = a, and so, from the graph, we see that a = 4.

Then we have the exponential y = 4(b)^(kx). Substitute 8 for y and 1 for x:

8 = 4(b)^(k), or 2 = b^k.

Then y = a(b)^(kx) becomes y = 4(b)^(kx) = 4[b^k]^x = 4[2]^x = y

The desired function is y = 4[2]^x.

Check this out. Does the point (0, 4) satisfy this function?

Is 4 = 4[2]^0 true? YES, it is.

Is 8 = 4[2]^1 true? Is 8 = 4(2) true? YES, it is