Exponential growth

Front

What is exponential growth?

Back

Exponential growth is a process where the quantity increases at a rate proportional to its current value, leading to growth that accelerates over time.

Front

How do you convert a percentage to a decimal?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 6.75% becomes 0.0675.

Front

What is the general formula for exponential growth?

Back

The general formula is y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time period.

Front

If an amount grows by 35% each year, what is the growth factor?

Back

The growth factor is 1.35.

Front

What does the y-intercept represent in an exponential function?

Back

The y-intercept represents the initial value of the function when x = 0.

Front

Write the exponential function for an initial amount of $15 growing at 35% per year.

Back

y = 15(1.35)^x.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.

Front

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

Back

To find the y-intercept, set x = 0 in the function and solve for y.

Front

What is the formula for calculating the future value in exponential growth?

Back

Future Value = Present Value * (1 + growth rate)^number of periods.

Front

If Samantha's hair grows at a rate of 14% per week, what is the growth factor?

Back

The growth factor is 1.14.