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marusya05 [52]
3 years ago
6

The table shows the distance Allison drove on one day of her vacation. Is the relationship between the distance and the time a p

roportional relationship? Did she drive at a constant speed? Complete the explanation.
Time (h) 1 2 3 4 5
Distance (mi) 55 100 165 280 250
Mathematics
1 answer:
Anuta_ua [19.1K]3 years ago
6 0

Answer:

we conclude that the relationship between distance and time is NOT proportional.

Hence, she did not drive at a constant speed.

Step-by-step explanation:

We know that when 'y' varies directly with 'x', we get the equation

y ∝ x

y = kx

k = y/x

where 'k' is called the constant of proportionality.

In our case, the table shows the distance Allison drove on one day of her vacation.

Time (h)              1         2        3          4        5

Distance (mi)       55    100     165     280    250

using the equation

k = y/x

susbtitute y = 55, x = 1

k = 55/1 = 55

substitute y = 100, x = 2

k = y/x

k = 100 / 2 = 50

substitute y = 165, x = 3

k = y/x

k = 165 / 3 = 55

substitute y = 280, x = 4

k = y/x

k = 280 / 4 = 70

substitute y = 250, x = 5

k = y/x

k = 250 / 5 = 50

It is clear that the value of 'k' does not remain constant.

Therefore, we conclude that the relationship between distance and time is NOT proportional.

Hence, she did not drive at a constant speed.

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Answer:

Step-by-step explanation:

The formula you need for this is

A(t)=P(1+\frac{r}{n})^{nt where

A(t) is the amount after a certain number of years has gone by,

P is the initial deposit,

r is the interest rate in decimal form,

n is the number of compoundings done per year, and

t is the amount of time in years.

For us,

A(t) = 11900

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r is .048

n is 12 (there are 12 months in a year)

t is our unknown. Filling in:

11900=250(1+\frac{.048}{12})^{(12)(t) which simplifies a bit to

11900=250(1_.004)^{(12t) . Now we'll divide both sides by 250:

47.6=(1.004)^{12t and then take the natural log of both sides to bring that t down out front:

ln(47.6)=ln(1.004)^{12t and then

ln(47.6) = 12t ln(1.004). Now divide both sides by ln(1.004) to isolate the 12t:

967.6383216 = 12t and divide both sides by `12 to get

t = 80.6 months which is 6.7 years

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