Exponential Models
Sam deposits $2500 into a savings acouunt that earns 6.3% interest compunded semi-annually. What is the interest rate as a decimal?
What os 0.063?
If there is no base written for a log it is automatically...?
Base 10
Where does the exponent go if I am expanding logarithms?
In front of the log
A negative in front of the whole functions means...
reflection in the x-axis
Is the following a geometric sequence?
3,6,12,24,48,....
yes
Tony invests $3250 at a 2.3% interest rate compounded monthly over a period of 5 years. How would this look in the compound interest formula?
What is... A= 3250(1+0.023/12)^12(5)
What is it called if e is the base of a logarithm?
Natural Log
Product property says that if two logs are being multiplied they expand to...?
Addition
Where do you put a vertical translation?
At the end of the function
What is the common ratio?
1,4,16,64,256,1024...
r=4
How would you set up the following into an equation?
Alex invests $5000 at a 4% interest rate compunded continuously for 10 years.
What is... A= 5000e^(0.004x10)
Exponent
Use properties of logarithms to rewrite this as a single log (condense).
3 log 4 − 2 log 7
log 64/49
Describe the transformation:
f (x) = 2x, g(x) = −2x − 3
Reflected over the x-axis
down three
Write an explicit rule for the following sequence.
2, 3, 4.5, 6.75, 10.125...
an=2(1.5)n-1
Solve the following:
Elizabeth deposits $1738 into a savings account that earns 7.8% interest, compunded annually, for 8 years. What is her total?
Rewrite the equation in exponential form.
log28=3
23=8
Use the properties of logarithms to expand the expression.
log (7/8)x
xlog 7- xlog 8
Describe the transformation
f (x) = e-x, g(x) = 3e-6x
Vertical stretch by 3
Horizontal shrink by 1/6
Given the explicit formula for a geometric sequence, find the first five terms.
an= 3n-1
1, 3, 9, 27, 81...
Solve the following:
A recent college graduate decides to open a credit card in order to pay for their upcoming trip across Europe. In order to get a card with a large enough credit limit to pay for their trip ($5,500), the student agrees to an interest rate of 38.99% compounded continuously. If no payments are made for an entire year, what will be the balance on the card rounded to the nearest penny?
$8122.58
Rewrite in log form.
42=16
Use the change-of-base formula to solve the following. Round to the nearest thousandth:
log57
1.209
Write the new function:
log12 x
Translation 5 units right, 2 units down, and reflection over the x-axis
-log12(x-5)-2
Given the recursive formula for a geometric sequence, find the common ratio and the first five terms.
an=an-1(2)
a1= 6
r= 2
6, 12, 24, 48, 96...