Exponential Decay and Derivatives

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x

• y=30(5000)^x

• y=5000(1.3)^x

• y=5000x^x

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

• Growth

• Decay

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor? Hint: decay factor is (1-r) where r is the rate as a decimal

• ^.08

• ^1.08

• .92

• 8

Is this exponential growth or decay?

• Growth

• Decay

What is a, the starting term, for the function: f(x) = 800(0.85)^x?

• 800

• 0.85

• 0.15

• x

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?

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?

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor?

• ^.08

• ^1.08

• .92

• 8

A flea medicine breaks down at a rate of 20% per hour. This is the rate of decay of the medicine. The initial dose is 60 milligrams. Which of the following represent the equation the models the amount of flea medicine left in an animal?

The value of a car depreciates exponentially. Identify the decay factor is the car was worth $20,000 initially and worth $15,000 after 1 year.

• 1.33

• 0.75

• 0.66

• 0.25