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Chapter 3: Problem 66

Describe the shape of a scatter plot that suggests modeling the data with an exponential function.

Short Answer

Expert verified
A scatter plot that suggests modeling the data with an exponential function would show a curve that rises or falls increasingly steeply. The points would not form a straight line. For an increasing exponential function, points start relatively low and increase gradually at first then steeply. For a decreasing exponential function, points start high and decrease gradually at first then steeply.

Step by step solution

01

Understanding Exponential Function

In an exponential function, the rate of change is proportional to the current value of the variable. This implies that the quantity increases or decreases rapidly. This rapid change is represented by a curve in a graph that rises or falls increasingly steeply.
02

Identifying Exponential Shape in Scatter Plot

If the scatter plot suggests an exponential function, the points on the plot would not form a straight line. Instead, they would form a curve that rises or falls increasingly steeply. This is because, in an exponential function, the rate of change increases or decreases exponentially.
03

Describing the Shape of Scatter Plot

The scatter plot suggesting an exponential function can be described as follows: If the function is an increasing exponential, the dots on the plot will start at a certain point on the y-axis where x=0 (assuming the constant 'a' in the exponential function). From there, the dots will increase gradually and then steeply as we move along the x-axis. Similarly, for a decreasing exponential function, the dots will start high and decrease gradually at first then decrease steeply as we move along the x-axis.

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Most popular questions from this chapter

You have \(\$ 10,000\) to invest. One bank pays \(5 \%\) interest compounded quarterly and a second bank pays \(4.5 \%\) interest compounded monthly. a. Use the formula for compound interest to write a function for the balance in each bank at any time \(t\) b. Use a graphing utility to graph both functions in an appropriate viewing rectangle. Based on the graphs, which bank offers the better return on your money?

Solve and graph the solution set on a number line: \(2 x^{2}+5 x<12 .\)

In Exercises \(125-132,\) use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution set. Verify this value by direct substitution into the equation. $$2^{x+1}=8$$

In Exercises \(125-132,\) use your graphing utility to graph each side of the equation in the same viewing rectangle. Then use the \(x\) -coordinate of the intersection point to find the equation's solution set. Verify this value by direct substitution into the equation. $$\log _{3}(3 x-2)=2$$

$$\text { Solve for } y: 7 x+3 y=18$$
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