Quiz about Exponential Curve Fitting

Question 1

Write the exponential regression equation for the data.

Accepted Answer

$$y=8.16(2.7)^x$$

Answer

$$y=81.6(2.7)^x$$

Answer

$$y=8.16(.27)^x$$

Answer

$$y=8.16(27)^x$$

Question 2

Which type of regression model does the scatter plot appear to show?

Accepted Answer

exponential

Answer

linear

Answer

quadratic

Question 3

Determine the curve of best fit.

Accepted Answer

$$y=0.95x^2-2.08x-0.75$$

Answer

$$y=-2.7x+7.4$$

Answer

$$y=-0.05x-3.26$$

Answer

$$y=0.95x^2+2.08x+0.75$$

Question 4

Fit an exponential model that would go through (4,9) and (5, 12).

Accepted Answer

$$y=2.84\left(1.33\right)^x$$

Answer

$$y=6.78x^{3.21}$$

Answer

$$y=1.8\left(5.6\right)^x$$

Answer

$$y=1.5x^{1.29}$$

Question 5

A chemist has a 100-gram sample of a radioactive material. He records the amount of radioactive material every week for 6 weeks and obtains the following data: Find the exponential model of the function.

Accepted Answer

y = 100(.87)^x

Answer

y = 100(8.7)^x

Answer

y = 100(1.87)^x

Answer

y = 100(.13)^x

Question 6

Which exponential function represents this table?

Accepted Answer

y=32(1/4)^x

Answer

y=512(1/4)^x

Answer

y=32(4)x

Answer

y=512(4)x

Question 7

Write the exponential regression equation for this data.

Accepted Answer

Y = 8.16(2.7)^X

Answer

Y = 81.6(2.7)^X

Answer

Y = 8.16(.27)^X

Answer

Y = 8.16(27)^X

Question 8

Choose all the equations that are exponential:

Accepted Answer

y = 5(1/3)^x

Accepted Answer

y = 2(8)x

Answer

y = 6x -5

Answer

f(x) = 3x²

Question 9

Jackson, Aria, and Harper are studying the population growth of a certain species of bacteria. They notice that the population growth does not seem to be linear, but rather, it seems to be growing at an increasing rate. Which concept could they use to model this type of growth?

Accepted Answer

They could use exponential regression, which models the relationship between equal-length input intervals and proportional output intervals.

Answer

They could use exponential regression, but it is only applicable to discrete data.

Answer

They could use exponential regression, which models the relationship between equal-length input intervals and linear differences in outputs.

Answer

They could use exponential regression, which is used to model linear relationships between variables.

Question 10

What function model best represents the data in the table?

Accepted Answer

exponential

Answer

linear

Answer

quadratic

Question 11

Using regression methods, write the function that BEST represents this data?

Accepted Answer

V = 15,000(0.9)^y

Answer

V = -1053y + 14,413

Answer

V = 60y² - 1,500y + 15,000

Answer

V = 100y² - 1,200y + 15,000

Question 12

Is the table linear, exponential, or quadratic?

Accepted Answer

Exponential

Answer

Linear

Answer

Quadratic

Answer

none of these

Question 13

Which statements describe the value of the car as a function of x, its age in years? Check all that apply.

Accepted Answer

The value, V, is represented by the equation V = 20,000(0.9)^x.

Accepted Answer

The domain is {x| x < 0}.

Accepted Answer

The relationship is exponential.

Answer

The relationship is quadratic.

Answer

The range is {V | 0 < V < 20,000}.

Question 14

What is the Exponential equation for the table?

Accepted Answer

y = 2(4)x

Answer

y = 4(2)x

Answer

y = 2(8)x

Answer

y = -2(4)^x

Question 15

A single person sent a text to 3 friends. Each person in this group of 3 people then sent the same text to several people. In each subsequent stage, each person who received a text sent the text to several new people. The table shows the number of texts sent at each stage.

Using regression methods, write the function that BEST represents this data?

Accepted Answer

f(x) = .9(4)^x

Answer

f(x) = 1.3(3)^x

Answer

f(x) = 152x - 176

Answer

f(x) = 73x² - 213x + 68

Question 16

Logarithmic functions are the inverse of...

Accepted Answer

Exponential Functions

Answer

Linear Functions

Answer

Quadratic Functions

Answer

Polynomial Functions

Exponential Curve Fitting

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