4.1
What is the formula for an exponential function?
Answer: f(t) = abt
What is the exponential growth equation?
f(x) = a(1+r)x
What is the compound interest formula?
A = P(1+r/n)nt
What is the compound continuous formula?
A=Pert
What's Ms. Salatas's middle name?
She doesn't have one :)
Solve without a calculator
eln(6.3)
6.3
What is the exponential decay equation?
f(x)=a(1-r)x
What is the continuous growth formula?
Q=a*ekt
the time period for an initial amount to be cut in half
Which day of the week does Graduation fall on?
Saturday
Rewrite in exponential form
log 100 = 2
102=100
In the year 2000, there were 10 squirrels living in a tree. Four years later, there are now 22 squirrels living in the tree. (assume linear growth) Find an equation for the number of squirrels. In terms of this scenario explain the variables.
y=3x+10
3 is how many squirrels are added per year
10 is the starting number of squirrels
Caffeine leaves the body at a continuous rate of 17% per hour. Write a formula for the amount of caffeine A present in the body (in mg), t hours after drinking coffee containing 100 mg of caffeine.
A= 100e-.17t
You have 3 million rubber balls and you continue finding rubber balls at a continuous rate of
B= 300e.007t, where B is the amount in millions and t is years since 2021. In 2030, how many millions of rubber balls will you have?
319.5 million
how many pages are in the notes doc for unit 4 (within 8)
42
State the growth factor and the formula:
The population, P, of ants in your kitchen starts at 10 and increases by 5% per day.
P=10(1+.05)t
growth factor = 1.05
In 2009 the population, P, of Kent, CT was 2,960 and had grown at a rate of 3.6% since the year 2000. Let t = 0 represent the year 2009.
Estimate what the pop will be in 2012?
2960(1+.036)3 = 3291
Compare the value of a 5000 dollar bank account being compounded at 4% interest weekly (52) versus quarterly (4).
quarterly= 5203.02
weekly= 5203.97
The population of City A begins with 50,000 people and grows at 3.5% per year. The population of City B begins with a larger population of 250,000 people but grows at the slower rate of 1.6% per year. Assuming that these growth rates hold constant, when will the populations of both cities be the same?
Around 87 years
Where did Ms. Salatas go to college?
Holy Cross
Polluted water is passed through a series of filters. Each filter removes 85% of the remaining impurities. Initially, the untreated water contains impurities at a level of 420 parts per million. Write a formula for L, the remaining level of impurities, after the water has been passed through a series of n filters.
L=420(1-.85)n
You are stranded on a deserted island. Luckily you are able to find 5 granola bars in your suitcase and every day, t, you nibble away 10% of your supply of granola bars, G.
Write a Formula for this equation and sketch a rough graph (get the correct shape, no exact points necessary)
G=5(1-.1)t
Has to show an exponential decay graph
After three years of being compounded at 3.2% monthly interest, your bank account reads $823098. What value did you initially deposit?
822,004
The U.S. population, P, in millions, is currently growing according to the formula: P = 299e.009t where t is in years since 2006. When is the population predicted to reach 350 million?
6÷2(1+2)
9