Exponential Growth and Decay (M)

What is the formula for an exponential function?

Answer explanation

Choose the formula that matches the exponential function format, which is y = ab^x.

What is the formula for exponential decay?

Answer explanation

The correct formula for exponential decay is y=a_1(1-r)^x, where 'a_1' is the initial value, 'r' is the rate of decay, and 'x' is the time variable.

What is the formula for exponential growth?

Answer explanation

The correct formula for exponential growth is y=a_1(1+r)^x, where a_1 is the initial amount, r is the growth rate, and x is the time period.

• Exponential Growth

• Exponential Decay

Answer explanation

The function y=7(1.54)^x represents exponential growth because the base (1.54) is greater than 1, causing the function to increase rapidly as x increases.

• 144%

• 2%

• 44%

• 1.44

Answer explanation

The growth rate in the function f(x)=2(1.44)^x is 44% because the base value is 1.44, which represents a 44% increase from the initial value of 1.

• Exponential Decay

• Exponential Growth

Answer explanation

The function y=2(.85)^x represents exponential decay because the base (0.85) is between 0 and 1, causing the function to decrease as x increases.

• 1200

• .15

• .85

• 6

Answer explanation

The decay rate is the value inside the parentheses, which is 0.85. Therefore, the correct answer is .15.

A population of 1500 deer decreases by 1.5% per year. At the end of 10 years, there will be approximately 1290 deer in the population. Which function can be used to determine the number of deer, y, in this population at the end of t years?

• y = 1500(1 - 0.015)^t
• y = 1500(0.015)^t
• y = 1500(1 - 1.5)^t

• y = 1500(1.5)^t

An antibiotic is introduced into a colony of 12,000 bacteria during a laboratory experiment. The colony is decreasing by 14.9% per minute. Which function can be used to model the number of bacteria in the colony after x minutes? (a)  

• f(x) = 12000( 14.9)^x

• f(x) = 12000(1 - 14.9)^x
• f(x) = 12000(1 - 0.0149)^x

• f(x) = 12000(1 - 0.149)x

There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 3.75% per month. At this rate of growth, which function can be used to determine the monthly cell phone sales x months after January? (a)  

• f(x) = 417(1 + 3.75)^x

• f(x) = 417(3.75)^x

• f(x) = 417(1 + .0375)x
• f(x) = 417(1 + 0.375)^x