Exponential: Growth and Decay

Front

What is the formula for exponential growth?

Back

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

Front

What is the formula for exponential decay?

Back

y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is time.

Front

What does the 'r' represent in the exponential growth formula?

Back

'r' represents the growth rate expressed as a decimal.

Front

How do you convert a percentage to a decimal for use in exponential equations?

Back

Divide the percentage by 100. For example, 7.5% becomes 0.075.

Front

What is the growth rate in the equation y = 35(1.075)^x?

Back

7.5%.

Front

What is the growth rate in the equation y = 5(1.27)^x?

Back

27%.

Front

How can you identify if an equation is linear or exponential?

Back

If the variable is in the exponent, it is exponential. If the variable is not in the exponent, it is linear.

Front

What type of function is y = 7(5/4)^x?

Back

Exponential Growth.

Front

What is the difference between linear and exponential functions?

Back

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

Front

What does the term 'decay' mean in exponential decay?

Back

Decay refers to a decrease in quantity over time, often expressed as a percentage.