Exponential Growth and Decay Review

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, represented by the equation y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity by a consistent percentage over time, represented by the equation y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

What does the base of an exponential function indicate?

Back

The base of an exponential function indicates the growth (if greater than 1) or decay (if between 0 and 1) rate of the function.

Front

How do you find the y-intercept of an exponential function?

Back

The y-intercept of an exponential function y = a(b)^x is found by evaluating the function at x = 0, which gives y = a.

Front

What is the formula for calculating exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the formula for calculating exponential decay?

Back

The formula for exponential decay is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

If a population of 1000 increases by 5% each year, what will be the population after 3 years?

Back

Using the formula y = 1000(1 + 0.05)^3, the population after 3 years will be approximately 1157.63.

Front

If a quantity decreases from 200 to 150 in one year, what is the decay rate?

Back

The decay rate can be calculated as r = (initial - final) / initial = (200 - 150) / 200 = 0.25 or 25%.

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.

Front

How do you determine the time it takes for a population to reach a certain size in exponential growth?

Back

To determine the time, rearrange the exponential growth formula to solve for t: t = log(y/a) / log(1 + r).