Formulas
What is the exponential growth formula?
A= A0(1+r)x
What does, A, r, and x represent in exponential growth formula?
A= starting amount
R= rate
x= time
Your car costs $42,500 when you purchased it in 2015. The value of the car decreases by 15% annually. What will be the value of the car in 2022?
$13,625
You borrowed $10,400 for 4 years at 12.7% and the interest is compound semi-annually. What is the total you will pay back?
$17,018.97
Write log232=5 in exponential form
25=32
What is the exponential decay formula?
A=A0(1-r)x
What does the A, r, and t represent in the exponential decay formula?
A= starting amount
r= rate
x= time
An investment of $75,000 increases at a rate of 12.5% per year. Find the value of the investment after 30 years.
$2,568,248
Your 2 year investment of $5,300 earns 2.9% and is compound annually. What will your total return be?
$5,611/86
Write log(3x4y−7)log(3x4y−7) in terms of simpler logarithms.
log(3)+4log(x)−7log(y)
What is the compound interest formula?
A=A0(1+r/n)nt
What does the A, P, r, n, and t represent
A= amount
P= principle
r= interest rate
n= number of times interest is compounded per year
t= time
A new car that sells for $18,000 depreciates 25% each year. Write a function that models the value of the car. Find the value of the car after 4 years.
$5,695
Your investment of $18,000 at 13.6% compound quarterly for 71/2 years will be worth how much?
$49,350.86
Combine: 2log4x+5log4y−12log4z2log4x+5log4y−12log4z into a single logarithm with a coefficient of one.
log4(x2y5√z)
A=Pert
What does A, O, e, r, and t represent in continuous compound formula?
A= amount
P= principle
e= constant
r= rate of interest
t= time
The bear population increases at a rate of 2% per year. There are 1573 bears this year. Write a function that models the bears population. How many bears will be there in 2 years?
1917 bears
Susan wants to invest her savings at a bank. Her new account has an interest rate of 6.5% compound continuously. She wants to use the money to buy a car in 36 months. How much should she invest if she wants to reach $7,500 in that time frame?
$6,171.26
Write log4(x−4y25√z)log4(x−4y2z5) in terms of simpler logarithms.
log4(x−4)−2log4(y)−15log4(z)
What is Newtons Law of Cooling formula?
T= C+(T0-C)ekt
What does T0, T, C, k, and t represent in Newtons Law of Cooling?
T0= initial temp
T= final temp
C= room temp (constant)
k= rate of temp change
t= time
A cup of fast food coffee is 180 degrees when poured. After 2 minutes in a room temp of 70 degrees, the coffee has cooled to 165 degrees. Find the time that it will take for the coffee too cool to 120 degrees.
10.7 minutes
How long will it take an investment of $10,000 to grow to $15,000 if it is invested at 9% compound continuously?
About 4.5 years
Combine 13loga−6logb+213loga−6logb+2 into a single logarithm with a coefficient of one.
log(1003√ab6)