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Helen [10]
3 years ago
11

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

Mathematics
1 answer:
Brilliant_brown [7]3 years ago
4 0

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

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