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Aleksandr [31]
3 years ago
10

A new car is purchased for 20300 dollars. The value of the car depreciates at 9.5% per year. What will the value of the car be,

to the nearest cent, after 11 years?
Mathematics
1 answer:
Iteru [2.4K]3 years ago
6 0
The starting value is 20,300, and the value is decreasing by 9.5% each year.

Because it decreases by 9.5% each year based on the previous amount, we use an exponential decay model.

A decrease by 9.5% corresponds to multiplying by 91.5% each year.

We write . We plug in 11 years for t.

A(t)=23000(0.915)^{t}\\\\A(11)=23000(0.915)^{11}\\\\A(11)=7671.18

$7,671.18
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In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample. To determine
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Answer:

(a)  0.2650

(b)  0.0111

(c)  0.0105

(d)  0.0006

Step-by-step explanation:

Given that:

In microbiology, colony-forming units (CFUs) are used to measure the number of microorganisms present in a sample.

Suppose that the number of CFUs that appear after incubation follows a Poisson distribution with mean μ = 15.       &;

If the area of the agar plate is 75cm²;

what is the probability  of observing fewer than 4 CFUs in a 25 cm² area of the plate.

We can determine the mean number of CFUs that appear on a 25cm² area of the plate as follows;

75cm²/25cm² = 3

Since;

mean  μ = 15  

mean number of CFUs that appear on a 25cm² = 15/3 = 5 CFUs

Thus ; the probability of observing fewer than 4 CFUs in a 25 cm² area of the plate is estimated as:

= P(X < 4)

Using the EXCEL FUNCTION ( = poisson.dist(3, 5, TRUE) )

we have ;

P(X < 4) = 0.2650

b) If you were to count the total number of CFUs in 5 plates, what is the probability you would observe more than 95 CFUs?

Given that the total number of CFUs = 5 plates; then the mean number of CFUs in 5 plates =  15×5 = 75 CFUs

The probability is therefore = P( X > 95 )

= 1 - P(X ≤ 95)

= 1 - poisson.dist(95,75,TRUE) ( by using the excel function)

= 0.0111

c) Repeat the probability calculation in part (b) but now use the normal approximation.

Let assume that the mean and the variance of the poisson distribution are equal

Then;

X \sim N (\mu = 75 , \sigma^2 = 75)

We are to repeated the probability calculation in part (b) from above;

So:

P( X > 95 )

use the normal approximation

From standard normal variable table:

P(Z > 2.3094)

Using normal table

P(Z > 2.3094) = 0.0105

(d)  Find the difference between this value and your answer in part (b).

So;

the difference between the value in part c and part b is;

=  0.0111 - 0.0105

= 6*10^{-4}

= 0.0006 to four decimal places

5 0
3 years ago
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