Question

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

Answer 1

Answer:

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

Step-by-step 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.