Question

The amount of money raised during an NPR telethon is listed below. DayMoney RaisedAbsolute changeRelative change 0300------------------ --------------- 1450 2600 3750 4900 Fill out the table above and determine if the growth each day is linear growth, exponential growth, or neither. If the growth is linear, enter the slope of the line rounded to the nearest tenth. If the growth is exponential, enter the growth factor of the exponential model as a DECIMAL rounded to the nearest tenth. (Growth factor = 1 r, where r is the relative change) If the growth is neither linear nor exponential, write -1 as the answer.

Answer 1

The increase in money raised during an NPR telethon shows linear growth, with a constant absolute change of 150 each day and a decreasing relative change percentage. The slope of the line representing the growth is 150.

Step-by-step explanation:

The problem asks us to fill out a table with the absolute change and relative change in the amount of money raised during each day of an NPR telethon and then determine the type of growth the data represents.

To find the absolute change, we subtract the previous day's amount from the current day's amount. The relative change is found by dividing the absolute change by the previous day's amount.

Absolute change:

• Day 1: 450 - 300 = 150
• Day 2: 600 - 450 = 150
• Day 3: 750 - 600 = 150
• Day 4: 900 - 750 = 150

Relative change (%):

• Day 1: (150 / 300) x 100 = 50%
• Day 2: (150 / 450) x 100 = 33.3%
• Day 3: (150 / 600) x 100 = 25%
• Day 4: (150 / 750) x 100 = 20%

Since the absolute change is constant but the relative change decreases each day, this suggests linear growth. The slope of the line representing the linear growth is the constant absolute change, which is 150.

Exponential growth would require a constant relative change, which is not the case here. Therefore, the growth is linear with a slope of 150 (rounded to the nearest tenth is still 150).