Exponential Growth and Decay

Front

What is the general form of an exponential growth equation?

Back

A = a(1 + r)^t, where A is the amount after time t, a is the initial amount, r is the growth rate, and t is time.

Front

What is the general form of an exponential decay equation?

Back

A = a(1 - r)^t, where A is the amount after time t, a is the initial amount, r is the decay rate, and t is time.

Front

How do you classify a model as exponential growth or decay?

Back

If the growth factor (1 + r) is greater than 1, it is growth; if (1 - r) is less than 1, it is decay.

Front

What is the growth factor if the growth rate is 80%?

Back

1.8, calculated as 1 + 0.80.

Front

If a population decreases by 6% per year, what is the decay factor?

Back

0.94, calculated as 1 - 0.06.

Front

How do you calculate the population after a certain number of years with exponential decay?

Back

Use the formula A = a(1 - r)^t, where A is the population after t years, a is the initial population, r is the decay rate, and t is time.

Front

What does the variable 'x' represent in the equation y = 300(0.6)^x for penicillin decay?

Back

The variable 'x' represents the number of days after the initial dose.

Front

What is the remaining amount of penicillin after 1 day if the initial dose is 300 mg and the decay factor is 0.6?

Back

180 mg, calculated as 300 * 0.6.

Front

What is the significance of the base in an exponential decay function?

Back

The base indicates the rate at which the quantity decreases; a base less than 1 signifies decay.

Front

How can you determine the amount remaining after multiple time periods in exponential decay?

Back

By applying the decay formula repeatedly or using the formula A = a(1 - r)^t.