Basic Maths 3

Tutorial 3
Questions for in-class tutorial:
Basic Maths:
1. Solve the following equations:
a) 2x2x+1 = 7
b) 20 = 40(1 – e-t)
c) log⁡(x^2-25)-0.5=1.5 + log⁡(x+5)
Application Questions:
1. Find the equilibrium price and quantity for the demand and supply functions
P_d = 50/(Q+2) and P_S = 10 + 2Q
2. A new model of popular television set is gradually replacing an earlier model. The projected sales (in thousands) for the old and new models are given by the equations
S_old = 4/(t+2) and S_new = 21/(12-t)
where time t is in months, S is the number of TVs sold (old and new models separately)
a) Calculate the number of TVs sold when t = 0 and 8
b) Calculate the time when sales are equal
Questions for self-study
1. The growth of demand for computer hardware in a college is given by the equation
Q = 200×〖1.025〗^t, where t is time in months
a) calculate the demand when t = 0 and 6 months.
b) calculate the time taken for the demand to increase to 300
2. A firm has a total cost function TC = √(4+6Q). If the firm charges a fixed price of 2 per unit sold:
a) write down the equation for total revenue
b) determine the break-even point

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