Exponential Functions
y = (2/3)x – 4
State the equation of the asymptote and whether it is a growth or decay function.
y = -4
Decay
Elba approximated that 190 people are going to attend the spring concert. The exact number of people attending was 214. Find the percent error.
Percent Error = 11.2%
What is the difference between simple interest and compound interest?
Simple interest = based on the original amount (stays the same over time)
Compound interest = based on the current amount (grows over time)
From your notes: The process of spreading payments over multiple periods is called ______.
amortization
Which grows faster, y = 3x or y = 4x? Justify your answer.
y = 4x
bigger base means the rate of growth is greater
A car is purchased for $25,000, and its value decreases by 7.5% per year. Write an equation for f(x), the value of the car after x years.
f(x) = 25000(0.925)x
Ryan thinks the cost of a video game is $65. However, the actual cost is $56.What is the percent error?
Percent Error = 16.1%
Sasha invests $4000 in a bank offering 2.8% interest compounded annually. How much money will Sasha have after 10 years? (round to nearest $)
$5272
A couple takes out a mortgage of $200,000 for a house. The mortgage is for 30 years at 2.5% interest per year. Find their monthly repayments. (round to nearest $)
$790
a) Is the function f(x) = 200(0.38)x growth or decay?
b) What is the percentage growth or decay?
b) 62%
The population growth of a town is modeled by the equation f(x) = 800(1.15)x, where x is the number of years since 2021. What will the population be in 2030?
2814
Johnny approximate the population of his small town to be 3,225 people. The exact population of his town is 4,057. What is the percent error?
Percent error = 20.5%
Ceyda invests $2000 in a bank offering 1.9% interest compounded monthly. After 10 years, how much money has she generated in interest? (round to nearest $)
$418
You take out a loan of $26,000 to buy a car. It is a 6-year loan with a 7% interest rate, compounded quarterly. Find the cost of your quarterly repayments. (round to nearest $)
$1336
Your money is invested at a 7% interest rate, compounded annually. The inflation rate is 1.5%. What percent is your investment growing by each year?
5.5%
The population growth of a town is modeled by the equation f(x) = 800(1.15)x, where x is time in years. How long will it take for the population to reach 10,000? (3 sig figs)
18.1 years
Sophia is working at a vet clinic. She knows the weight of a cat to be 8.5 pounds. When she weighed the cat, she found that her approximate weight had an error of 12%. Find the possible approximate weights of the cat.
Approximate Weight = 9.52 pounds or 7.48 pounds
Yassir invests $3500 in a bank that offers interest at 3.2% per year compounded monthly. How many months will it take for his original amount of money to double? (round to nearest whole number)
260
Isaac took out a loan for $50,000 at an annual interest rate of 6%, compounded monthly. He repays $1000 every month. How many months will it take him to fully pay back the loan? (round to nearest whole #)
58
On the Finance app, when should PV be positive and when should it be negative?
Positive when you're receiving money (e.g taking out a loan)
Negative when you're putting money into an investment (e.g. compound interest problems)
The mass of a decaying substance over time is modeled by the equation f(x) = 35400(0.97)x, where x is time in minutes. How long will it take for substance to reduces to one third of its original mass? (3 sig figs)
36.1 years
Ginny wants to buy a new gaming device for her nephew. She approximates the cost to be $250. If the percent error is 8% above the exact value, what is the exact price of the device?
Actual Value = $231.48
Jovita invests $1200 in a bank that offers interest at a rate of r% per annum compounded quarterly. Her money doubles in 10 years. Find the value for r. (3 sig figs)
r = 6.99
Chelsea takes out a loan for $170,000 at an interest rate of 5% per year, to be paid in monthly installments. If it is a 10-year loan, how much will Chelsea pay in total over the life of the loan? (round to nearest thousand $)
$216,000
Draw a picture of a moose who loves math.
?