Question

1)

a) Find the corresponding demand​ function, given the following total revenue function

TR= -13Q²+40Q P=?

b) Given the total revenue and total cost​ functions, TR= -2Q²+21Q and TC= 5Q+30

​i) find the value of Q for which the firm breaks even

​ii) find the value of Q for which the firm maximises profit.

c) Find the value of x which satisfies 900(1.6)^x=90000 ​(Use logarithms to base 10 to calculate your​ answer.)

d) Use the rules of logarithm to express the following as a single logarithm.

4 ln x + 3 ln y - ln z

The expression of the single logarithm is ?

e) The value of a product reduces exponentially with​ age, so its value y after t years can be modelled by the formula y=A e^-at

If the product had a value of $50,000 when it was new and was worth ​$37,000 after 2 years, find the values of A and a.

A=

f) The value of an​ investment, V​, grows exponentially over time t with V=400e^0.002t. Show that a graph of ln(V) plotted againts t is a straight line and state the EXACT value of its slope and intercept on the vertical axis.

Intercept= ln(?) and slope = (?)

Answer 1