Name

  1. Using R, create a plot of the following cubic cost function. Start at a quantity of 0 and end at a quantity of 25. What are costs when Q = 20?

\[ C(Q) = 0.5Q^{3} - 15Q^{2}+177Q+3600 \]

Q <- seq(from=0,to=25,by=1)

cost <- 0.5*Q^3 - 15*Q^2 + 177*Q + 3600

plot(cost~Q,type="l")

cost[21]
## [1] 5140
  1. Create a plot for a person who starts with $10,000 in an account at 8% interest. Plot the future value on the vertical axis and time on the horizontal axis. How long will it take for the value of the investment to reach $20,000?
t <- seq(from=0,to=40,by=1)

FV <- 10000*(1.08)^t

plot(FV~t,type="l")

Around 8 or 9 years the investment would reach 20,000.

t <- seq(from=0,to=50,by=1)
FV <- 10000*(1+0.8)^t
plot(FV~t,type="l")