Exponential Growth and Decay

Exponential Growth and Decay

y = a(b)^x

The 'b' is (1 - r)

DECAY: y = a(1 - r)^x

Decay

y = a(b)^x

The 'b' is (1 + r)

GROWTH: y = a(1 + r)^x

​Growth

Exponential Equation

Steps for Writing Exponential Equations

1: Decide if the problem is describing exponential growth or decay. ("increase" = growth, "decrease" = decay)

2: Convert the growth or decay percentage to a decimal. This decimal is your r value. Ex: 23% = .23 and 5% = .05

3: Write your exponential equation. a is your starting value.

GROWTH: y = a(1 + r)^x

DECAY: y = a(1 - r)^x

Multiple Choice

Mr. Hatcherson currently brings in an annual salary of $55,000 and anticipates a raise of 5% every year.

Is this problem describing exponential growth or decay?

• Growth

• Decay

Fill in the Blanks

Mr. Hatcherson currently brings in an annual salary of $55,000 and anticipates a raise of 5% every year.

Convert the growth percentage to a decimal.

Fill in the Blanks

Mr. Hatcherson currently brings in an annual salary of $55,000 and anticipates a raise of 5% every year.

We now know that our r value is 0.05. What is our a value? (a is the starting value)

Draw

Mr. Hatcherson currently brings in an annual salary of $55,000 and anticipates a raise of 5% every year.

Okay, now we know this is growth, r = 0.05, and a = 55,000. Let's put it all together in an exponential equation.

Great job! Let's try another example.

Multiple Choice

Mr. Hatcherson got a promotion because of all of his students passed the STAAR Test and is now a real-deal teacher. He purchased a Hellcat for $90,000 and anticipates that it will depreciate 15% every year.

Is this problem describing exponential growth or decay?

• Growth

• Decay

Fill in the Blanks

Mr. Hatcherson got a promotion because of all of his students passed the STAAR Test and is now a real-deal teacher. He purchased a Hellcat for $90,000 and anticipates that it will depreciate 15% every year.

Convert the decay percentage to a decimal.

Fill in the Blanks

Mr. Hatcherson got a promotion because of all of his students passed the STAAR Test and is now a real-deal teacher. He purchased a Hellcat for $90,000 and anticipates that it will depreciate 15% every year.

We now know that our r value is 0.15. What is our a value? (a is the starting value)

Draw

Mr. Hatcherson got a promotion because of all of his students passed the STAAR Test and is now a real-deal teacher. He purchased a Hellcat for $90,000 and anticipates that it will depreciate 15% every year.

Okay, now we know this is decay, r = 0.15, and a = 90,000. Let's put it all together in an exponential equation.

BONUS QUESTION!!!!!!!!!!

Fill in the Blanks

Mr. Hatcherson got a promotion because of all of his students passed the STAAR Test and is now a real-deal teacher. He purchased a Hellcat for $90,000 and anticipates that it will depreciate 15% every year.

Even though Mr. Hatcherson now has the coolest car on campus, what will the car be worth after 5 years?

(Hint): Round your answer to the nearest whole number