Question

Complete the table. What kind of decay is this?the options are linear or exponential

Answer 1

a) 430 b)

Step-by-step explanation:

The initial area = 490 square foot

Each day, we have a decrease of 60 square foot of painting

for the 1st day:

The amount remaining = 490 - 60 = 430 square ft

for 2nd day:

The amount remaining = 430 - 60 = 370 square ft

The equaton:

The amount remaining = 490 - 60(d)

were d = number of days

3rd day: d = 3

The amount remaining = 490 - 60(3) = 310 square ft

4th day: d = 4

The amount remaining = 490 - 60(4) = 250 square ft

5th day: d = 5

The amount remaining = 490 - 60(5) = 190 square ft

To determine the decay, we can find the change in area:

`\begin{gathered} \text{let use points (d, A)}\colon\text{ (1, 490) and (2, 430)} \\ \text{slope = }\frac{490-\text{ 430}}{2-1}\text{ = 60/1 = 60} \\ \\ \text{points (d, A)}\colon\text{ (2, 430) and (3, 370)} \\ \text{slope = }(430-370)/(3-2)\text{ = 60/1 = 60} \end{gathered}`

The rate of change is constant. It is a linear decay as the graph of th points will show a straight line with negative slope