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

There are 4 cups in a quart and 4 quarts in a ganon. jug of water? . how many cups are in a 5-gallon jug of water?

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?

According to the general equation for conditional probability if p(anb)=3/7 and p(b)=7/8 what is p(a i b)