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

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

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. Exponential: f(x)=a e^(k x), k>0
D. Logistic: f(x)=a/(1+b e^(-k x))
E. Polynomial, not quadratic
F. Quadratic: f(x)=a x^2+b x+c

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

Solution

Solution Steps

Step 1: Observing the scatterplot trend

The scatterplot shows a decreasing trend. As the x-value (Day) increases, the y-value (# of fruit flies) decreases. The decrease is not linear, but appears to be exponential decay.

Step 2: Identifying the matching function

An exponential decay function is of the form f(x) = ae^-kx, where k > 0. This corresponds to option A.