Question

Which function is a shrink of the exponential growth
function shown on the graph?.

Answer 1

Explanation:

An exponential function is represented by function,

`y = a * {b}^(x)`

Where a is the y intercept and b is the growth factor.

The graph passes through (0,1) which is our y intercept so a=1

Know let find b.

The graph pass through (1,3) so plug in 1 for x and 3 for y.

`3 = a * 3 {}^(1)`

`a = 1`

So our base function is

`y = 1 * 3 {}^(x)`

In order for this function to shrink, we must shift the y intercept such that it is less than 1 but greater than -1.

So the only option is

`y = (1)/(2) (3) {}^(x)`

Because 1/2<1