Question

The table below shows the sale, in dollars, at Jacobs store over a period of five months:

Month sale
1. 1,000
2. 1,050
3. 1,102.50
4. 1,157.63
5. 1,215.51
Did the number of people at Jacobs store increase linearly or exponentially?
A) Linearly, shows a constant percentage in sales per month
B) Exponentially, shows a constant percentage per month
C) Linearly, by an equal factor for an increase in months
D) Exponentially, table shows and increase in sales for an equal increase in months

Answer 1

B: Exponentially, because the table shows a constant percentage increase in sales per month.

Explanation:

As we go through the days, the number of dollars that Jacobs earns does not increase at a constant (or linear) rate, instead beginning to sharply slope upwards the higher the number before it. This is because there is a percentage being added to it, rather than a solid number. On a graph, this equation would start slow, then begin to curve upwards, steeper and steeper with each day.

I hope this helps all future people viewing this question!

Answer 2

The table which is depiction of monthly sale in Dollars over a period of 5 months:

1. 1,000------(1)

2. 1,050--------(2)

3. 1,102.50-----(3)

4. 1,157.63--------(4)

5. 1,215.51----------(5)

As we know slope of line joining two points (p,q) and (a,b) is :

`(b-q)/(a-p)`

Slope between point 1 and point 2 is = 50-------a

Slope between point 2 and point 3 is = 52.50-------b

Slope between point 3 and point 4 is = 55.13---------c

Slope between point 4 and point 5 is = 57.88----------d

b= a + 2.50, c= b+2.63, d=c+2.75

% between two months =
`\frac{\text{Coming  month-Previous month}}{Previous Month} *100`

% increase between first two months=5%

% increase between Second and third month =5%

% increase between third and fourth month =Less than 5%

As you can see from above observation , first three options A,B,C are incorrect.

Option (D) Exponentially, table shows and increase in sales for an equal increase in months, Satisfies the above condition.