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GREYUIT
1 month ago
8

The population of Nottingham highschool can be modeled using the equation p (t) =2,600 (0.96)^t, where t is the number of years

since 2000,
is the population of nottingham increasing or decreasing Explain how you can tell using the equation
Mathematics
1 answer:
Zina [12.3K]1 month ago
7 0
Equation:
p(t) =2,600 (0.96)^t

When t = 1,

p(1) =2,600 (0.96)^1 = 2496

When t = 2,

p (t) =2,600 (0.96)^2 = 2396.16

Answer: The population is on the decline. This can be determined from the equation since the exponent's value for a number less than one diminishes as the exponent increases.

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Answer:

The likelihood that the number of drivers is at most 18 is 0.381.

Step-by-step explanation:

We are provided with the following details in the question:

The quantity of drivers traveling between a specific origin and destination in a set time frame follows a Poisson distribution characterized by the parameter μ = 20.

  • The Poisson distribution defines the probability of a certain number of events taking place over a specific period, based on the mean frequency of those events.
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a) P(number of drivers will be at most 18)

Equation:

P(X =k) = \displaystyle\frac{\mu^k e^{-\mu}}{k!}\\\\ \mu \text{ is the mean of the distribution}

P( x \leq 18) =P(x=0) + P(x =1) + P(x = 2) +... + P(x = 18)\\\\= \displaystyle\frac{20^0 e^{-20}}{0!} + \displaystyle\frac{20^1 e^{-20}}{1!} +...+ \displaystyle\frac{20^{18} e^{-20}}{18!}\\\\ = 0.381

So, 0.381 represents the probability that the number of drivers will be at most 18.

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