Question

for the data set shown by the table,
a. create a scatter plot for the data.
b. use the scatter plot to determine whether an
exponential function, logarithmic function, or a linear
function is the best choice for modeling the data.
b. a(n) function best models the data.

Explanation:

Step1: Analyze the growth rate

For a linear function, the rate of change is constant. For an exponential function, the ratio of consecutive terms is approximately constant.
Let's check the ratios of the number of books:
\(\frac{35}{26}\approx1.35\), \(\frac{42}{35} = 1.2\), \(\frac{55}{42}\approx1.31\), \(\frac{83}{55}\approx1.51\), \(\frac{112}{83}\approx1.35\)
The ratios are not exactly the same but are in a relatively close range.
For a linear function, the differences: \(35 - 26=9\), \(42 - 35 = 7\), \(55 - 42=13\), \(83 - 55 = 28\), \(112 - 83=29\) are not constant.
For a logarithmic function \(y = a + b\ln(x)\), the growth rate slows down. But here the number of books is increasing at a non - slowing rate (the differences are not getting smaller in a way that would suggest a logarithmic model).

Answer:

exponential