Samantha puts an initial $500 into a savings account. The account has a 4% annual compound interest rate. What is the equation that best represents Samantha's account?
Hint: Use the formula y = P(1 + r)x.
y = 500(1.4)x
y = 500(0.04)x
y = 500(1.04)x
y = 500(0.4)x
The correct equation that represents Samantha's account is:
y = 500(1.04)x
Which of the following options is an equivalent function to f(x) = 3(2)3x?
f(x) = 3(8)x
f(x) = 24x
f(x) = 27(8)x
f(x) = 3(8x)
To find the equivalent function, we simplify f(x) = 3(2)^3x.
Since 2^3 = 8, the simplified function becomes f(x) = 3(8)x.
Therefore, the equivalent function is f(x) = 3(8)x.
Rewrite the function f of x equals 6 times one fourth to the 2 times x power using properties of exponents.
a. f of x equals 36 times one fourth to the x power
b. f of x equals 36 times one sixteenth to the x power
c. f of x equals 6 times one sixteenth to the x power
d. f of x equals 6 times two eighths to the x power
write answer in equation form
The correct answer is:
c. f(x) = 6 * (1/16)^x
The average annual salary of the employees of a company in the year 2005 was $70,000. It increased by the same factor each year, and in 2006, the average annual salary was $82,000. Let y represent the average annual salary, in thousand dollars, after x years since 2005. Which of the following best represents the relationship between x and y?
y = 70(1.17)x
y = 82(1.17)x
y = 70(2.2)x
y = 82(2.2)x
The correct equation that represents the relationship between x and y, given the information provided, is:
y = 70(1.17)x
To pay for a home improvement project that totals $11,000, Genesis is choosing between taking out a simple interest bank loan at 6% for 3 years or paying with a credit card that compounds monthly at an annual rate of 16% for 6 years. Which plan would give Genesis the lowest monthly payment?
a. The monthly credit card payment would be $396.49, which is lower than the monthly payment on the bank loan.
b. The monthly payment on a bank loan would be $360.56, which is lower than the monthly credit card payment.
c. The monthly credit card payment would be $354.44, which is lower than the monthly payment on the bank loan.
d. The monthly payment on a bank loan would be $323.89, which is lower than the monthly credit card payment.
To determine which plan would give Genesis the lowest monthly payment, we need to calculate the monthly payments for both options.
For the bank loan at 6% for 3 years, we need to calculate the monthly payment using the formula:
Monthly payment = Total loan amount / (Number of months * Monthly interest rate)
Monthly interest rate = Annual interest rate / 12
Plugging in the values for the bank loan:
Total loan amount = $11,000
Annual interest rate = 6%
Number of years = 3
Monthly interest rate = 6% / 12 = 0.06 / 12 = 0.005
Number of months = 3 * 12 = 36
Monthly payment = $11,000 / (36 * 0.005) = $11,000 / 0.18 = $61,111.11 / 18 = $3,395.61
For the credit card at 16% compounded monthly for 6 years, we can use the formula for the monthly payment of a loan with compound interest:
Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Number of months))
Plugging in the values for the credit card:
Loan amount = $11,000
Annual interest rate = 16%
Number of years = 6
Monthly interest rate = 16% / 12 = 0.16 / 12 = 0.01333
Number of months = 6 * 12 = 72
Monthly payment = ($11,000 * 0.01333) / (1 - (1 + 0.01333)^(-72)) = $146.53 / (1 - 0.949959) = $146.53 / 0.050041 = $2,925.31
Comparing the two options:
Option a: The monthly credit card payment would be $396.49, which is higher than the monthly payment on the bank loan.
Option b: The monthly payment on a bank loan would be $360.56, which is lower than the monthly credit card payment.
Option c: The monthly credit card payment would be $354.44, which is lower than the monthly payment on the bank loan.
Option d: The monthly payment on a bank loan would be $323.89, which is lower than the monthly credit card payment.
Therefore, the correct answer is option d. The monthly payment on a bank loan would be $323.89, which is lower than the monthly credit card payment.
The price of bronze has increased by 10% per year from 2000. In the year 2000, Harry bought a bronze medal for $120. Which of the following equations can be used to represent the price of the medal x years after 2000?
y = 120(0.9)x
y = 10(120)x
y = 120(1.1)x
y = 10(1.1)x