How would I do these?
6. The speed of sound is approximately 1.2 × 10³ km/h.
How long does it take for sound to travel 7.2 × 10²
km? Write your answer in minutes.
7. Evaluate the function below over the domain {-1, 0,
1, 2}. As the values of the domain increase, do the
values of the function increase or decrease?
y = (3/4)ˣ
8. Suppose an investment of $5,000 doubles every 12
years. How much is the investment worth after 36
years? After 48 years?
Write and solve an exponential equation.
9. Does the function represent exponential growth or
exponential decay? Identify the growth or decay
factor.
= 9 ∙ (1/2)ˣ
10. You deposit $520 in an account with 4% interest
compounded monthly. What is the balance in the
account after 5 years?
6. d = V*T.
720 = 1200*T.
Solve for T and Convert from hours to minutes.
10. P = Po(1+r)^t.
r = 0.04/12 = 0.00333/mo.
t = 5yrs. * 12mo/yr. = 60 mo.
Po = $520.
6. To find out how long it takes for sound to travel a certain distance, you can use the formula: time = distance / speed.
Given that the speed of sound is approximately 1.2 × 10³ km/h and the distance is 7.2 × 10² km, we can substitute these values into the formula:
time = 7.2 × 10² km / (1.2 × 10³ km/h)
To simplify this calculation, we divide the values:
time = 0.6 × 10² h = 60 h
Since the question asks for the answer in minutes, we can convert 60 hours into minutes by multiplying by 60:
time = 60 h × 60 min/h = 3600 min
Therefore, it takes 3600 minutes for sound to travel a distance of 7.2 × 10² km.
7. To evaluate the function y = (3/4)ˣ over the domain {-1, 0, 1, 2}, you simply substitute each value into the function and calculate the corresponding output.
For x = -1:
y = (3/4)^(-1) = 4/3
For x = 0:
y = (3/4)^0 = 1
For x = 1:
y = (3/4)^1 = 3/4
For x = 2:
y = (3/4)^2 = 9/16
As the values of the domain increase from -1 to 2, the values of the function decrease. This is because the base of the exponential function (3/4) is less than 1, which causes the function to decay as x increases.
8. Since the investment doubles every 12 years, the growth rate can be expressed as (1 + r)² = 2, where r is the annual growth rate.
Simplifying the equation, we have:
(1 + r)² = 2
1 + r = √2
r = √2 - 1
To find the investment worth after a certain number of years, we use the formula: worth = initial investment × (1 + r)^t, where t is the number of years.
After 36 years:
worth = $5,000 × (1 + (√2 - 1))^36
After 48 years:
worth = $5,000 × (1 + (√2 - 1))^48
By plugging in the values and solving the exponential equations, you can find the worth of the investment after 36 and 48 years.
9. The function y = 9 ∙ (1/2)ˣ represents exponential decay.
In an exponential growth or decay function of the form y = a * bˣ, the base (b) determines whether it is exponential growth or decay. If the base is greater than 1, it represents exponential growth. If the base is between 0 and 1, it represents exponential decay.
In this case, the base (1/2) is between 0 and 1, so the function represents exponential decay.
10. To calculate the balance in an account after a specific time, we use the formula for compound interest: A = P * (1 + r/n)^(nt), where A is the final balance, P is the principal amount (initial deposit), r is the annual interest rate (expressed as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
Given that you deposit $520, the interest rate is 4% (0.04 as a decimal), and the interest is compounded monthly (n = 12), we can calculate the balance after 5 years:
A = $520 * (1 + 0.04/12)^(12*5)
By plugging in the values and computing the equation, you can find the final balance in the account after 5 years.