Having trouble with questions 1, 3, 4
exercise 9.05 modelling exponential functions
1
a full 30 000 l cylindrical rainwater tank has sprung a leak in the seam at the
bottom of the tank. as the water leaks out, the pressure of water decreases. this means
that the tank leaks more slowly over time. the level of water in the tank is given by
l = 295 x 0.97^t cm, where t is the time in hours from the start of the leak. the leak
was discovered 3 hours after it started.
a what is the diameter of the tank?
b how much water leaked out before the leak was discovered?
c how long will it take for 5000 l to leak out?
what is the level after 2 hours?
3 the population of rabbits in an area increases by an average of 50% every month.
how long would it take two rabbits to overrun an area at a population of 3000 rabbits?
4 a sample of radioactive material loses 4% of its radioactivity per annum. calculate