Question

the number of burgers and milkshakes sold by a restaurant since it was opened are represented by the following tables:

burgers
time (months) units sold
1 353
4 691
7 1034
10 1374
13 1713

milkshakes
time (months) units sold
1 259
4 380
7 501
10 622
13 744

determine whether the data described in the tables is best modeled by a linear function or an exponential function.

linear function exponential function
burgers
milkshakes

Explanation:

Step1: Check burger linear differences

Calculate the change in units sold between consecutive time points (time increases by 3 months each interval):
$691 - 353 = 338$
$1034 - 691 = 343$
$1374 - 1034 = 340$
$1713 - 1374 = 339$

Step2: Check burger exponential ratios

Calculate the ratio of units sold for consecutive intervals:
$\frac{691}{353} \approx 1.96$
$\frac{1034}{691} \approx 1.496$
$\frac{1374}{1034} \approx 1.329$
$\frac{1713}{1374} \approx 1.247$

Step3: Check milkshake linear differences

Calculate the change in units sold between consecutive time points:
$380 - 259 = 121$
$501 - 380 = 121$
$622 - 501 = 121$
$744 - 622 = 122$

Step4: Check milkshake exponential ratios

Calculate the ratio of units sold for consecutive intervals:
$\frac{380}{259} \approx 1.467$
$\frac{501}{380} \approx 1.318$
$\frac{622}{501} \approx 1.242$
$\frac{744}{622} \approx 1.196$

Answer:

Burgers: Linear function
Milkshakes: Linear function