Answer:
1. The required function is [tex]f(x)=16(\frac{1}{2})^x[/tex].
2. The required function is [tex]y=\frac{5}{4}x-3[/tex].
3. The required function is [tex]h(x)=3(2)^x[/tex].
Step-by-step explanation:
1.
The exponential function is defined as
[tex]f(x)=ab^x[/tex]
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
[tex]16(\frac{1}{2})^x[/tex]
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
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-3)}{4-0}=\frac{5}{4}[/tex]
The slope intercept form of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
The required function is
[tex]y=\frac{5}{4}x-3[/tex]
3.
The exponential function is defined as
[tex]f(x)=ab^x[/tex]
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
[tex]h(x)=3(2)^x[/tex]
