Exponential Review

Front

What is exponential decay?

Back

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

Front

How do you calculate the future value of a quantity experiencing exponential growth?

Back

The future value can be calculated using the formula y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What does the variable 'a' represent in the equation y = a(1 + r)^t?

Back

The variable 'a' represents the initial amount or value before any growth or decay occurs.

Front

If a population is modeled by P = 6191(1.04)^t, what does 1.04 represent?

Back

The value 1.04 represents a growth factor, indicating a 4% increase in population each year.

Front

What is the formula for calculating the number of subscribers after a percentage decrease?

Back

The formula is y = a(1 - r)^t, where 'a' is the initial number of subscribers, 'r' is the rate of decrease, and 't' is the number of years.

Front

How do you round a number to the nearest whole number?

Back

To round a number to the nearest whole number, look at the digit to the right of the decimal point: if it's 5 or greater, round up; if it's less than 5, round down.

Front

What is the significance of the exponent 't' in exponential functions?

Back

The exponent 't' represents time, indicating how many periods of growth or decay have occurred.

Front

If a quantity decreases by 10% each year, what is the decay factor?

Back

The decay factor is 0.90, which is calculated as 1 - 0.10.

Front

What does a 15% increase in farmers' markets imply about the growth rate?

Back

A 15% increase implies that the growth rate 'r' in the exponential growth formula is 0.15.

Front

How can you determine the initial population from a model like P = 6191(1.04)^t?

Back

The initial population can be determined by evaluating the model at t = 0, which gives P = 6191.