Graphing Exponential Eqns
Where is the asymptote for y = 2(3)x - 3
y = 0
23 = 8 write as a logarithm
log28 = 3
You’ve just landed your first summer job. You decide to take $2,500 of your earnings and put it into a savings account to save up for a high-end gaming PC.
The bank offers an interest rate of 6% per year, and the interest is compounded quarterly. How much money will you have in 5 years?
$3,367.14
Write as a logarithm: e5 = 148.41
ln 148.41 = 5
Which 2023 movie based on a video game franchise became the first "game movie" to surpass $1 billion at the box office?
Super Mario Brothers Movie
State the transformations:
y=1/2(3)x - 5
log 1000 = 3
Write as an exponential equation.
103 = 1000
When Sofia was born, her grandparents deposited $5,000 into a special savings account to help pay for her future education. The account earns 4.5% annual interest, compounded daily.
Sofia is now 18 years old and is ready to withdraw the money for college.
How much interest did the account earn over the 18 years?
$6,239
Write as an exponential equation:
ln 10 = 2.3
e2.3 = 10
In the Marvel Cinematic Universe, what is the name of the fictional African nation ruled by the Black Panther?
Wakanda
1) decay
2) moved left 4 units
3) reflected over x-axis
y = -(any pos # < 1)x + 4
Evaluate without a calculator: log 10
1
Caitlin wants to buy a used car in exactly 4 years. She has done the math and knows she will need $12,000 to cover the cost of the car, taxes, and registration.
She finds a long-term Certificate of Deposit (CD) account that offers an annual interest rate of 5%, compounded monthly. How much money should she deposit today to reach her goal?
$9,828.86
Evaluate without a calculator: ln e26
26
This artist became the youngest person to win all four main Grammy categories in one year (Best New Artist, Record, Album, and Song of the Year).
Billie Eilish
f(x) = -2x + 3
Domain: all real numbers
Range: y < 3
Evaluate without a calculator: log1/2(8)
-3
A local landscaping company took out a small business loan of $12,000 to purchase a new commercial lawnmower and trailer. After exactly 6 years, the loan was paid off in one final lump sum of $18,500.
The loan agreement stated that interest was compounded semi-annually. What was the annual interest rate?
7.33%
An investor wants to have exactly $1,000,000 in their retirement account in 35 years. They have found an aggressive growth fund that historically yields a 9% annual interest rate that compounds continuously.
How much money must the investor deposit today as a single lump sum to reach their $1,000,000 goal?
$42,852.14
Graph: f(x) = 2(3)x - 1 - 3
moved one unit to the right, stretch by a factor of 2
growth graph, down 3
Evalute: log9(-81)
Undefined
The Chen family has $40,000 saved up in a high-yield investment account. They have found a neighborhood they love and want to wait until their account balance reaches $60,000 before they withdraw the money to use as a down payment on a new home.
The account earns a 5.5% annual interest rate, and the interest is compounded quarterly.
How many years will it take for the account to reach at least $60,000?
7.42 years
An early investor put $5,000 into a promising tech startup. After 8 years, the company was acquired, and the investor’s share was worth $8,250.
The investment's growth is modeled using continuous compounding.
What was the annual interest rate for this investment?
6.26%
Taylor Swift’s "Eras Tour" became the first concert tour in history to gross over $1 billion. However, which legendary female artist held the previous record for the highest-grossing tour?
Madonna