Question

Which of the statements describes a situation which models growth or decay by an equal factor over equal

intervals?
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A. A water tank is filled at a rate of 2 gallons per minute.
B. A vine grows 6 inches every week.
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C. A species of fly doubles its population every month during the summer.
D. A car increases its distance from a garage as it travels at a constant speed of 25 miles per hour.

Answer 1

The statement that describes a situation that can be modeled as a growth or decay over equal interval is;

C. A species of fly doubles its population every month during the summer

Explanation:

We have for exponential growth or decay, the following equation;

Exponential growth or decay;

`y = a \cdot b^t`

Where;

a = The initial amount of the item

1 + r = The rate of growth in percentage

b = The growth or decay factor

t = The time

For exponential decay, we have;

0 < b < 1

b = 1 - r

`y = a \cdot(1 - r)^t`

For exponential growth, we have;

b > 1

b = 1 + r

`y = a \cdot(1 + r)^t`

Therefore, given that the number of the fly population doubles every month, we have the growth rate, r as 100%, which is written as 100/100 = 1, to give;

`y = a \cdot(1 + 1)^t = a \cdot(2)^t`

Which is expressed as an exponential growth by an equal factor of, r, over equal intervals of, t, time.