Answer:
The value of r is 0.451
The percentage decrease is about 45.1%
Step-by-step explanation:
The given exponential function is
Using the exponent rule,
Now the value of
Thus, we can rewrite the function as
Therefore, the function in form
The value of r is 0.451
The percentage decrease is about 0.451 ×100 = 45.1%
Answer:
The probability of driving to the store is 0.969
Step-by-step explanation:
The remaining part of the question is attached
Solution
There are only two possible ways –
a) Route comprising of bridges 123
b) Route comprising of bridge 45
Probability of success while traveling through Route 123 = P(Bridge 1 open) x P(Bridge 2 open) x P(Bridge 3 open)
= 0.9 x 0.92 x 0.91
= 0.75348
P(Route 123 is closed) = 1 - 0.75348 = 0.24652
Probability of success while traveling through Route 45 =
P(Bridge 4 open) x P(Bridge 5 open)
= 0.94 x 0.93
= 0.8742
P(Route 45 is closed) = 1 - 0.8742 = 0.1258
To travel to store, atleast one route from 123 and 45 should be open.
Probability that you can drive to store :
= P(atleast one route from 123 and 45 is open)
= 1 - P(Both routes 123 and 45 are closed)
= 1 - P(123 is closed)*P(45 is closed)
= 1 - 0.24652*0.1258
= 1 - 0.031012216
= 0.968987784
~ 0.969
