Question

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

Answer 1

Step-by-step explanation:

An exponential function is represented by function,

$y = a \times {b}^{x}$

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.

$3 = a \times 3 {}^{1}$

$a = 1$

So our base function is

$y = 1 \times 3 {}^{x}$

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

$y = \frac{1}{2} (3) {}^{x}$

Because 1/2<1