Questions: For the scatterplot on the right, determine which, if any, of these functions might be used as a model for the data. Quadratic: f(x)=a x^2+b x+c Polynomial, not quadratic Exponential: f(x)=a e^(k x), k>0 Exponential: f(x)=a e^(-k x), k>0 Logarithmic: f(x)=a+b ln x Logistic: f(x)=a/(1+b e^(-k x)) Which of the functions above might be used as a model for the data? A. Exponential: f(x)=a e^(-k x), k>0 B. Logarithmic: f(x)=a+b ln x C. Logistic: f(x)=a/(1+b e^(-k x)) D. Quadratic: f(x)=a x^2+b x+c E. Polynomial, not quadratic F. Exponential: f(x)=a e^(k x), k>0

For the scatterplot on the right, determine which, if any, of these functions might be used as a model for the data.

Quadratic: f(x)=a x^2+b x+c

Polynomial, not quadratic

Exponential: f(x)=a e^(k x), k>0

Exponential: f(x)=a e^(-k x), k>0

Logarithmic: f(x)=a+b ln x

Logistic: f(x)=a/(1+b e^(-k x))

Which of the functions above might be used as a model for the data?

A. Exponential: f(x)=a e^(-k x), k>0

B. Logarithmic: f(x)=a+b ln x

C. Logistic: f(x)=a/(1+b e^(-k x))

D. Quadratic: f(x)=a x^2+b x+c

E. Polynomial, not quadratic

F. Exponential: f(x)=a e^(k x), k>0

Transcript text: For the scatterplot on the right, determine which, if any, of these functions might be used as a model for the data. Quadratic: $f(x)=a x^{2}+b x+c$ Polynomial, not quadratic Exponential: $f(x)=a e^{k x}, k>0$ Exponential: $f(x)=a e^{-k x}, k>0$ Logarithmic: $f(x)=a+b \ln x$ Logistic: $f(x)=\frac{a}{1+b e^{-k x}}$ Which of the functions above might be used as a model for the data? A. Exponential: $f(x)=a e^{-k x}, \mathrm{k}>0$ B. Logarithmic: $f(x)=a+b \ln x$ C. Logistic: $f(x)=\frac{a}{1+b e^{-k x}}$ D. Quadratic: $f(x)=a x^{2}+b x+c$ E. Polynomial, not quadratic F. Exponential: $f(x)=a e^{k x}, k>0$

Solution

Solution Steps

Step 1: Identify the type of data trend

Examine the scatterplot to determine the trend of the data. The data points show a decreasing trend that levels off as the x-values increase.

Step 2: Match the trend with function types

Compare the observed trend with the given function types:

Exponential: Decreases rapidly and then levels off.
Logarithmic: Increases rapidly and then levels off.
Logistic: S-shaped curve, levels off at both ends.
Quadratic: Parabolic shape, either opens upwards or downwards.
Polynomial, not quadratic: Various shapes, not necessarily fitting the observed trend.

Step 3: Select the appropriate function

The scatterplot shows a decreasing trend that levels off, which matches the behavior of an exponential function.