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True [87]
3 years ago
5

The value of a collector’s item is expected to increase exponentially each year. the item is purchased for $500. after 2 years,

the item is worth $551.25. which equation represents y, the value of the item after x years? y = 500(0.05)x y = 500(1.05)x y = 500(0.1025)x y = 500(1.1025)x
Mathematics
1 answer:
sasho [114]3 years ago
8 0

Answer:

y=500(1.05)^x

Step-by-step explanation:

The standard form for an exponential equation is

y=a(b)^x

We have 2 unknowns, a and b, but that's all good because we have 2 (x, y) coordinates we can utilize in order to find a and b.  In our coordinate pair, x is the number of years gone by and y is the value after that number of years.  The problem tells us that an item was purchased for $500.  That translates to "before any time has gone by, the initial value of the item is $500".  In other words, with x being time, no time has gone by, so x = 0.  When x = 0, y = 500.  (0, 500).  Do the same for the next set of numbers.  When x = 2 years gone by, the value is $551.25, so the coordinate is (2, 551.25).  Now we use them to find a.  Use the first coordinate:

500=a(b)^0

Anything raised to the 0 power = 1, therefore:

500 = a(1) and a = 500.

Now onto the next coordinate point using the a value we just found:

551.25 = 500(b)^2

Divide both sides by 500 to get

1.1025=b^2

so b = 1.05.

Now we have the values for a and b, so we fill in:

y = 500(1.05)^x

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fredd [130]

Answer:

4

Step-by-step explanation:

4 is the base of the equation and then as it goes on, you add 2* the point in the sequence -1

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2 years ago
This table shows values represented by an exponential function.
Bad White [126]

Answer:

a = 2 , f(2)=9

b = 4 , f(4)=64

And replacing the data into the average rate formula we got:

m = \frac{64-9}{4-2}= 27.5

And then the best answer for this case would be:

C. 27.5

Step-by-step explanation:

For this cae we know that the average rate of change of a function is given by this general expresion:

m = \frac{f(b) -f(a)}{b-a}

For this special case from the info of the table we have:

a = 2 , f(2)=9

b = 4 , f(4)=64

And replacing the data into the average rate formula we got:

m = \frac{64-9}{4-2}= 27.5

And then the best answer for this case would be:

C. 27.5

7 0
3 years ago
A gardener measured the heights of two plants at the end of every week. The function y=3x+8.5 gives the hight of plant a in cent
MAVERICK [17]

Answer:

12 weeks

Step-by-step explanation:

Step one:

given data

let the heights of the plants be y

and the number of weeks be x

Plant A

y=3x+8.5--------------1

Plant B

y=2.5x+14.5----------2

Required

The number of weeks taken for both plants to have the same height

,equate the two expressions above

3x+8.5=2.5x+14.5

3x-2.5x=14.5-8.5

0.5x= 6

divide both sides by 0.5

x= 6/0.5

x= 12 weeks

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Answer:

D because even though the flat fee is 150 paying 5$ a hour it will cost less

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Of the 58 employees in a firm, 8 are considered support staff, and 7 of the employees have more than five years of experience. A
polet [3.4K]

Using statistical concepts, it is found that the number of outcomes that are possible for the complement of the union of Events J and K is of 43.

<h3>What is the union of events J and K?</h3>

It means that at least one of event J or event K is true, hence, it is composed by employees that are either considered support staff(less than 5 years of experience) or employees that have more than five years of experience, combining a total of 7 + 8 = 15 employees.

<h3>What is the complement?</h3>

The total number of outcomes of the union of J and K, plus the complement, add to the total number of 58, hence:

15 + x = 58

x = 43.

The number of outcomes that are possible for the complement of the union of Events J and K is of 43.

More can be learned about complementary events at brainly.com/question/9752956

6 0
2 years ago
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