To determine whether the number of shoppers at Jacob's store increased linearly or exponentially, we can analyze the pattern of the increase in the number of shoppers over the given months.
Let's look at the table provided:
- Month 1: 50 shoppers
- Month 2: 250 shoppers
- Month 3: 1250 shoppers
- Month 4: 6250 shoppers
- Month 5: 31250 shoppers
To see if the increase is linear or exponential, let's check the ratios between the number of shoppers in consecutive months:
1. From Month 1 to Month 2:
[tex]\[
\frac{250}{50} = 5
\][/tex]
2. From Month 2 to Month 3:
[tex]\[
\frac{1250}{250} = 5
\][/tex]
3. From Month 3 to Month 4:
[tex]\[
\frac{6250}{1250} = 5
\][/tex]
4. From Month 4 to Month 5:
[tex]\[
\frac{31250}{6250} = 5
\][/tex]
We observe that the ratio between the number of shoppers for each consecutive month is consistent, with each month having 5 times more shoppers than the previous month.
This consistent multiplicative factor indicates that the number of shoppers is increasing exponentially.
Therefore, the answer is:
[tex]\[
\text{Exponentially, because the table shows the number of shoppers increases by an equal factor for an equal increase in months.}
\][/tex]
