#1 Amount of investment. Area of a painting of p dollar for t years at simple in

Question

#1
Amount of investment. Area of a painting of p dollar for t years at simple interest rate r is given by A=P+prt
a. Rewrite the formula by factoring out the greatest common factor on the right hand side.
b. B. Find A $8300 is invested for 3 years at a simple interest rate of 15%




#2
Demands for pools. Tropical pools sell above ground model for P dollar each. The monthly revenue for this model is given by the formula
R(p) = -0.08p^2+300p.
Revenue is the product price p and the demand (quality sold).
a. Factor out of the price on the right hand side of the formula.
b. B. write a formula D(p) for the monthly demand.
c. Find D (3000).
d. Use graph to estimate price at which the revenue is 0
e. what is the maximum revenue?

Explanation / Answer

A). rewrite this formula by factoring out the greatest common factor on the right hand side.

Pull out the "P":

A = P(1 + rt)

B). find A if $8300 is invested for 3 years at a simple interest rate of 15%.

Plug in P = 8300, t = 3, r = 0.15:

A = 8300*(1 + 0.15*3)

A = 8300*(1.45)

A = $12035

a) Factor out the price on the right-hand side of the formula.

R = p(-0.08p + 300)

b) What is an expression for the monthly demand?

D = R/p

D = -0.08p + 300

c) What is the monthly demand for this pool when the price is $3000?

D = -0.08*3000 + 300

D = 60

d) Use the graph to estimate the price at which the revenue is maximized. Approximately how many pools will be sold monthly at this price?

Maximum is at the vertex...

-b/2a

= -300/(2*-0.08)

Revenue is maximized when P = 1875 (you should see this on the graph that you have)

When P = 1875:

D = -0.08*P + 300

D = 150

e) What is the approximate maximum revenue?

The maximum revenue is:

-0.08*1875^2 + 300*1875

= 281250

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.