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)