Exponential Growth/Decay
The proper format for a basic exponential function.
What is y=(b)x
A Minecraft village has 28 doors. This amount triples every day. This is the number of doors after 5 days.
6,804 doors
In 2015, a cell phone was $600. The price decreased by 12.5% each year. The value of the phone in 2018.
What is $401.44
The approximate value of e
What is 2.7182
In the equation y=a(b)x, a does this.
What is vertical stretch/compression.
The value of a computer, after 8 years, that cost $1500 and that goes down in value by 3% every year.
What is $1175.62
Rabbits have a population of 8 million back in 1999. Their rate of increase is 1.5% each quarter. What will be the population by the end of 2024?
What is about 35.456 million rabbits
Tess has a stack of 20 cookies. Each hour, her friend Mason eats half of the remaining cookies. The number of cookies remaining after 3 hours.
The equation that calculates e?
What is e=(1+1/n)n
The transformation described by g(x)=2(1/2)x-2.
What is down 2 and vertical stretch by a factor of 2.
When the base is 1/2, we can expect the graph to be an exponential form of this.
What is decay
You see a new camera that you like but it costs $680 and is a bit too expensive. You decide to wait 3 years before purchasing it. If the cost decreases by 2.5% each year, the camera will be this price.
What is $630.26
Every year the butterfly population is cut in half. The starting population is 10,000. The number of years it will take to have less than 1000 butterflies.
What is after 3.32 years.
$368 is deposited into an account that pays 6.7% compounded continuously. This is the amount in the account after 10 years.
What is $719.16
Describe the effect of the transformation of the parent function to g(x)=3(1/4)x+1+2
What is
-up 2
-left 1
-stretched vertically by factor of 3
2.79 is decaying by 14% each quarter. The amount left after 1.5 years.
about 1.13
The population of a town is 3,500 and doubles every decade. The number of people will there be in 12 years.
What is 8040 or 8041 people?
400g of a medicine has a half-life of 5 hours. The length of time it take to completely dissolve. (or at have 0.1% or less of the original amount - 0.4g)
What is 50 hours
You are playing on a game show where the amount of cash you have previously won will either decrease or increase by 2% for 2 years. You entered in $1606 and just your luck, you got the decrease roll. The amount you will have left when they finally give you your winnings after the 2 years is this.
What is $1542.40
The domain of g(x)=1/3(e)x-1
What is All Real numbers
(or negative infinity to positive infinity)
The regression equation for an exponential function that goes through the points (0, 98) ; (1, 71); (2, 52)
What is y=98(0.73)^x
The panda population in China is currently 10,000 and is decreasing at a rate of 13% per year. In 10 years there is expected to be this many pandas.
What is 2484 pandas.
You have $100 in a bank account (at the best bank in the world!). Every month the balance doubles. How much will be in the account after 1 year and 11 months.
What is $838,860,800
Carl has $100 and invests it into a bank that offers continuous compounding at an interest rate of 5%. Find the balance after 3 years.
What is $116.183
This exponential function y=7ex=4 is shifted down by 9 and moved to the left by 6.
What is y=7ex+10-9