1,The sum of $3000 is placed in the savings account. If money worth 6% compounded semi annually, what is
he balance in the account after 7 year? Assume no other deposit and no withdrawals are made.2,The demand function of a manufacturers production is P=1000-2q where P is the price (per unit) when Q units
are demanded (per week) by consumers. Find the marginal revenue when 250 units are produced
To answer the first question, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (balance) in the account
P = the principal amount (initial deposit)
r = annual interest rate
n = number of times compounding occurs per year
t = number of years
In this case, the principal amount (P) is $3000, the annual interest rate (r) is 6%, and compounding occurs semiannually, so the number of times compounding per year (n) is 2.
Let's calculate the final amount after 7 years:
A = 3000(1 + 0.06/2)^(2 * 7)
A = 3000(1 + 0.03)^14
A = 3000(1.03)^14
A ≈ $4426.91
Therefore, the balance in the account after 7 years will be approximately $4426.91.
Now, let's move on to the second question:
The demand function given is P = 1000 - 2q, where P is the price per unit and q is the quantity demanded per week by customers.
To find the marginal revenue when 250 units are produced, we need to find the derivative of the demand function with respect to q, and then evaluate it at q = 250.
Marginal revenue (MR) is the rate of change of revenue with respect to the quantity produced.
Revenue (R) is given by the formula: R = P * q
Now, let's find the derivative of the revenue function with respect to q:
R = (1000 - 2q) * q
R = 1000q - 2q^2
To find MR, we differentiate R with respect to q:
MR = dR/dq = 1000 - 4q
Now, plug in q = 250 into the marginal revenue function:
MR(250) = 1000 - 4(250)
MR(250) = 1000 - 1000
MR(250) = 0
Therefore, the marginal revenue when producing 250 units is 0.