Question

P(t) 177.39 x 0.9231 Note that probabilities are numbers between O (will never occur) and 1 (will always occur). Obtain a graph of the function on the interval [O, 80]. Also, make a table that gives the average rate of change AP/At on the following eight intervals: [0, 10], [10, 20], [20, 30],... [70, 80]

Answer 1

$Q4:~\frac{1}{1+77.39\times 0.923^t}=0.7\Rightarrow 1+77.39\times 0.923^t=10/7\\\\ or,~77.39\times 0.923^t=3/7~or,~0.923^t=3/(7*77.39)~or,\\ ~t=\log(3/(7*77.39))/\log(0.923)=64.8\\ Answer:~64.8~year\\ Q5.~Average~rate=\frac{P(40)-P(30)}{40-30}\\ P(40)=\frac{1}{77.39\times 0.923^{40}}=0.3186\\ P(30)=\frac{1}{77.39\times 0.923^{30}}=0.1430\\ Average~rate=(0.3186-0.1430)/10=0.0176~per~year$