Question

Each function below describes how something changes. Use the description to determine which function(s) describe exponential growth or decay.

A. The power of a turbine is proportional to the cube of wind speed.
B. The population decreases by 12 % each year.
C. The volume of a sphere triples every minute.
D. The pollution increases at a rate of 11 grams per day.
E. The thickness of ice increases by fifty millimeters each day.

Answer 1

Explanation:

A) Here power and wind speed have a cubic relation with each other

we consider power as P and wind speed as S then, by given relation

P = KS^3

which is cubic relation and not exponential.

B) Let us assume the population of the town be 100 initially.

It decreases by 12% annually. So, next year population will be 88

then, it becomes 77.44 and so on. After two years 100(0.88)^2, 100(0.88)^3 in three years. Therefore, this is an example of exponential decrease.

C) Let initial volume be 100 units.

then in 1 min time , it will be 300.

in 2 min, it will be 900

in 3 min, it will be 2700.

This is exponential.

Note: any thing that becomes doubled/halved/tripled etc, is always exponential.

D) The pollution increases at a rate of 11 grams per day :

Now, this rate is a constant rate of increase and is therefore NOT exponential, it is in fact a linear increase.

E) The thickness of ice increases by fifty millimeters each day is again a linear increase and not exponential. AS it is a constant increase each day.