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
Rewrite the following equation in exponential form:
log5(125) = 3
53 = 125
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
Rewrite the following equation in logarithmic form:
4x = 12
log4(12) = x
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
Find x if 6x = 300. (3 sig figs)
x = 3.18
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
Find x if ln(x) = 4. (3 sig figs)
x = 54.6
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
The pH of a solution is given by the formula pH = -4log(C), where C is the hydrogen ion concentration in a solution (in moles per liter). Find the hydrogen ion concentration in a solution with pH 3.7. (3 sig figs)
.119 moles per liter
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.
?