Exponential Growth vs Decay

Exponential Growth vs Decay

Graphs, Calculations, Practice

​Learning Intention:

I can recognize an exponential function and can calculate values using y = a * b^x​

Exponential Growth Question:

A rich family member dies and leaves you money in the will. But, here's the catch! You can either take $1,000,000 in one lump sum today OR....receive $0.01 (one penny) today and it be doubled every day for 30 days like a typical month? Which would you choose?

We will let you think on this!!!

Now on with the lesson!

​Pay it Forward

​Do a good deed for 3 people and each of them does good deeds for 3 more people.

Exponential Growth vs. Decay

This video shows what exponential growth on a table and a graph looks like.

It also shows what exponential decay on a table and a graph looks like.

Multiple Choice

Which graph represents exponential decay?

Multiple Choice

Which graph represents exponential growth?

Multiple Choice

$$y=\left(\frac{1}{5}\right)^x$$ Is this exponential growth or decay?

• Growth

• Decay

Multiple Choice

What type of function is f(x) = 2^x ? 

(could also be written as f(x)= 1*2^x meaning start value is "1")

• exponential growth 

• linear equation

• exponential decay 

• linear inequality 

Multiple Choice

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

• y = 15(35)^x

• y = 15(1.35)^x

• y = 15(0.35)^x

• y = 35(1.15)^x

Multiple Choice

Give the rate of growth:
y = 5(1.27)^x

• 127%

• 27%

• 5

Multiple Choice

Is this exponential growth or decay?

• Growth

• Decay

Multiple Choice

The population of turtles is doubling every 3 months.  If there are 400 turtles now, how many will there be in 2 years?  (Choose equation)

• y = 400(2)²

• y = 400(2)⁶

• y = 400(2)⁸

• y = 400 + 2(8)

Multiple Choice

A city has a population of 21,517 based on a census taken in 1998. If the population is expected to grow by 11% annually, what will the population be in the year 2030?

• 606,900

• 517

• 492,573

• None of these

Multiple Choice

Your 2 year investment of $5,300 earns 2.9% and is compounded annually.  What will your total return be?

• $5,304.46

• $5,611.86

• $5,613.28

• $8,819.73

Multiple Choice

Give the rate of decay:
y = 35(0.65)^x

• 35%

• 65%

• .35%

• 165%

Multiple Choice

Which of the following is an example of exponential decay?

• y = 3(5)^x

• y = .5(5)^x

• y = 2(.5)^x

• y = 8(1)^x

Multiple Choice

Is the pictured graph exponential growth, exponential decay, linear growth, or none?  

• Exponential Growth
• Exponential Decay
• Linear Growth
• None of the above

Multiple Choice

The attendance at the art museum at the New Year’s opening was 250 people. The attendance has been increasing at a rate of 3% each month. How many people will attend by the end of a year?

• 356

• 265

• 5825

• 1329

Multiple Choice

Pick the equation that is exponential growth

• y=2(0.5)^x

• y = 0.5(2)^x

• y = .5x - 2

• y = 2x + .5 

Multiple Choice

$$y=7\left(1.2\right)^x$$ Is this exponential growth or decay?

• Growth, because of 7

• Decay, because of 1.2

• Growth because of 1.2

• Decay because of 7

Multiple Choice

The population of Bloom Falls, Mass. (population 937) is slowly moving to a bigger city.
Every year the population drops by 4.5%. What is the population after 3 years?

• 1,069 people

• 894 people

• 816 people

• 854 people

Multiple Choice

A sailboat that costs $5,950 decreases in value by 11% per year. How much will the boat be worth after 6 years?

• $5,884.00

• $5,178.97

• $2,992.96

• $2,957.04

Multiple Choice

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^t where t is the number of years since 1990. What was the population in 1990? 

• 0 people

• It doesn't say

• I don't know

• 6191

Multiple Choice

The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.

• y=1400(1.09)^x

• y=1.09(1400)^x

• y=1400(.91)^x

• y=1.09^x

Multiple Choice

In the compound interest formula A=P(1+r)^t what does the A stand for?

• The amount of interest

• The total amount

• The interest rate

• The time

Multiple Choice

In the compound interest formula A=P(1+r)^t what does the P stand for?

• The time

• The total amount

• The principal amount (original amount)

• The interest rate

Multiple Choice

Daniel invests $360 in a bank account that is compounded annually for 8 years with an interest rate of 5.5%. What will be the total amount in the account after the 8 years?

• $625.88

• $950.12

• $315.45

• $552.49

Multiple Choice

Semi-Annually means how many times a year?

• 4

• 2

• 1

• 6

Multiple Choice

Zach's parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded semi-annually, what will be the balance after 18 years?

• $6,273.50

• $6,314.08

• $6,385.72

• $6,427.94

Multiple Choice

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

• 9766

• 9006

• 9765

• 5433

Multiple Choice

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

Multiple Choice

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

• 14327

• 4309

• 839

• 7680

Multiple Choice

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

• $23,219.72

• $136.72

• $51,710.94

• $16,710.94

Multiple Choice

In 1985, there were 285 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per year after 1985. How many cell phone subscribers were in Centerville in 1994?

• OVERFLOW

• 1994

• 1000

• 43871

Multiple Choice

The population of Townville is decreasing at a rate of 6% each year. If the starting population was 7,000 what equation represents the current population after x number of years?

• $$f\left(x\right)=7000\left(0.6\right)^x$$  

• $$f\left(x\right)=7000\left(0.4\right)^x$$  

• $$f\left(x\right)=7000\left(0.06\right)^x$$  

• $$f\left(x\right)=7000\left(0.94\right)^x$$  

Exponential Growth Question:

A rich family member dies and leaves you money in the will. But, here's the catch! You can either take $1,000,000 in one lump sum today OR....receive $0.01 (one penny) today and it be doubled every day for 30 days like a typical month? Which would you choose?

MAKE A DECISION AND BACK IT UP WITH AN EQUATION AND SOME REASONS.