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Alex787 [66]
2 years ago
6

A chain of retail computer stores opened 2 stores in its first year of operation. After 8 years of operation, the chain consiste

d of 206 stores. If the number of stores opening per year is increasing at an exponential rate, identify the continuous rate of growth. Round k to the nearest hundredth. *
Mathematics
1 answer:
Helen [10]2 years ago
4 0

Answer:

0.66

Step-by-step explanation:

The exponential growth equation is expressed as;

S(t) = S0e^kt

S(t) is the number of stores after t years

S0 is the initial number of stores

If a chain of retail computer stores opened 2 stores in its first year of operation then at t = 1, S(t) = 2. Substitute into the equation;

2 = S0e^k(1)

2 = S0e^k .... 1

Also if after 8 years of operation, the chain consisted of 206 stores, this means at t = 8, S(t) = 206. Substitute into the equation;

206 = S0e^k(1)

206 = S0e^8k .... 2

Next is to calculate the value of k

Divide equation 2 by 1;

\frac{206}{2} = \frac{S0e^{8k} }{S0e^k }\\103 =   e^{7k}\\apply \ ln \ to \ both \ sides\\ln103 = lne^{7k}\\ln103 = 7k\\k = \frac{ln103}{7}\\k = \frac{4.6347}{7} \\k =  0.6621

Hence the value of k to the nearest hundredth is 0.66

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Mika is a local farmer who is interested in how often residents in her town go to a farmer's market each month. She surveys 124
TEA [102]

Answer:

The margin of error is of 0.3012, and it means that we should be 99% confident that the population mean would be within 0.3012 of the sample mean.

Step-by-step explanation:

Margin of error

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation and n is the size of the sample.

Standard deviation of 1.3

This means that \sigma = 1.3

She surveys 124 families

This means that n = 124

Margin of error and meaning:

M = z\frac{\sigma}{\sqrt{n}}

M = 2.58\frac{1.3}{\sqrt{124}}

M = 0.3012

The margin of error is of 0.3012, and it means that we should be 99% confident that the population mean would be within 0.3012 of the sample mean.

6 0
2 years ago
Please help.........
faust18 [17]
The answer for PA is 60/13. This is found by
The area of the rectangle is 60, therefore, the big triangle areas are 30 each. We know that the hypotenuse is 13, so therefore, we get
1/2(13*PA) = 30. This then simplifies to 
13 * PA = 60, which then turns into 
PA = 60/13.

Hope this helps and have a nice day:)
5 0
3 years ago
A. How much higher is 500 than 400 m?
Nonamiya [84]
A 100 m
B 900m
C -5,100m
D- 8,800
6 0
2 years ago
What is required for an electric charge to flow through a wire?
slamgirl [31]
A difference in electric potential
7 0
2 years ago
Read 2 more answers
Sarah the cheetah ran 100 meters at a speed of 16.8 meters per second. An olympian ran the 100-meter dash in 9.6 seconds. How mu
EastWind [94]

Given that Sarah the cheetah ran 100 meters at a speed of 16.8 meters per second.

An olympian ran the 100-meter dash in 9.6 seconds.

Then speed of olympian = distance/ time = 100 meter/ 9.6 seconds = 100 meter/ 9.6 seconds = 10.4166666667 meter/ seconds


whis is approx 10.42 meter/seconds

Now we need to find about how much faster was Sarah the cheetah’s speed, to the nearest tenth of a meter per second.

16.8-10.42 = 6.38 = 6.4

Hence speed of Sarah the cheetah's is approx 6.4 meter per second more than the speed of olympian.

4 0
3 years ago
Read 2 more answers
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