Question

1-What is the exponential function graphed in the figure?

Answer 1

Answer:

1. The required function is $f(x)=16(\frac{1}{2})^x$.

2. The required function is $y=\frac{5}{4}x-3$.

3. The required function is $h(x)=3(2)^x$.

Step-by-step explanation:

1.

The exponential function is defined as

$f(x)=ab^x$

Where, a is initial value and b is growth rate.

The y-intercept of the given graph is (0,16) and the graph shows a decreasing function. So, the initial value is 16 and growth rate is less than 1.

The required function is

$16(\frac{1}{2})^x$

2.

The y-intercept of the function is (0,-3).

The line is passing through (0,-3) and (4,2). The slope of the line is

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-3)}{4-0}=\frac{5}{4}$

The slope intercept form of a line is

$y=mx+b$

Where, m is slope and b is y-intercept.

The required function is

$y=\frac{5}{4}x-3$

3.

The exponential function is defined as

$f(x)=ab^x$

Where, a is initial value and b is growth rate.

The y-intercept of the given graph is (0,3) and the graph shows a increasing function. So, the initial value is 3 and growth rate is greater than 1.

The required function is

 $h(x)=3(2)^x$