Answer to Question #334645 in Algebra for deekay

Question

2. The growth in demand for computer hardware in a college is given by the equation t Q = )025.1(200 , where t is in months.

i) Calculate the demand when t = 0, 3, 6, 10 months.

ii) Calculate the time taken for the demand to increase to 300.

iii) Graph the demand for t = 0 to 30, hence confirm the answers to (i) and (ii).

Answer 1

$$Q(t)=200(1.025)^t$$

i)

$$Q(0)=200(1.025)^0=200$$

$$Q(3)=200(1.025)^3=215.378$$

$$Q(6)=200(1.025)^6=231.939$$

$$Q(10)=200(1.025)^{10}=256.017$$

ii)

$$200(1.025)^t=300$$

$$t=\dfrac{\ln1.5}{\ln1.025}$$

$$t=16.42\ months$$

iii)