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goldfiish [28.3K]
3 years ago
7

Madame Pickney has a rather extensive art collection and the overall value of her collection has been increasing each year. Thre

e years ago, her collection was worth $500,000. Two years ago, the value of the collection was $550,000 and last year, the collection was valued at $605,000.
Assume that the rate at which Madame Pickney’s art collection’s value increase remains the same as it has been for the last three years. The value of the art collection can be represented by a geometric sequence. The value of the collection three years ago is considered the first term in the sequence.
Write an explicit rule which can be used to determine the value of her art collection n years after that. Use this to determine the value of her collection 10 years after she started tracking its worth rounded to the nearest dollar.

PLEASE answer the value of her collections 10 years after she started tracking its worth.
Mathematics
2 answers:
grigory [225]3 years ago
6 0

Answer:

About $1,178,974

Step-by-step explanation:

Alright, the sequence we have right now is:

500,000       550,000      605,000

We want to find the common ratio, so let's divide 550,000 by 500,000 and see if we get the same value as 605,000 divided by 550,000:

550,000/500,000 = 1.1

605,000/550,000 = 1.1

Now, we know that r = 1.1. We also know the first term is: a_1 = 500,000.

We use the explicit rule of a geometric sequence:

a_n=a_1*r^{n-1}

Here, we want to find a_{10} , which means that n = 10. We know r and a_1, so we just plug in these values:

a_{10}=500,000*(1.1)^{10-1}=500,000*(1.1)^{9} ≈ 1,178,973.85 ≈ 1,178,974

Thus, the answer is about $1,178,974.

Hope this helps!

Anastasy [175]3 years ago
6 0

Answer:

Value = 500000 × (1.1^n)

$1,296,871

Step-by-step explanation:

a = 500000

r = 550000 ÷ 500000 = 1.1

1st term is the initial year:

n years after that is the "n+1"th term

Value = 500000 × (1.1^n)

n = 10

500000(1.1¹⁰)

1,296,871.23005

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Work Shown:

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3 years ago
The product of a positive number and 2 more than that number is 63 find the numbers
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Would someone mind explaining this?
Nesterboy [21]

Answer:

3?

Step-by-step explanation:

i think that because it's multiplying by 3.

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This is the only way i could think of helping in some sort of way! I'm sorry if it's wrong! (´。_。`)

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A private jet can fly 1,095 miles in 3 hours with a tailwind but only 987 miles in 3 hours into a headwind find the speed of the
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Answer:

The speed of the jet is 347 mph and the  speed of the wind is 18 mph.

Step-by-step explanation:

We have the following:

x = the speed of the jet in still air.

y = the speed of the wind

we know that the speed is equal to:

v = d / t

therefore the distance would be:

d = v * t

if we replace with the information of the exercise we have:

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we must solve this system of equations, add both equations and we are left:

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Im trying to figure out how to find the length of an equilateral triangle
gulaghasi [49]

All 3 sides of an equilateral triangle are the same.

Set up an equation with two sides equaling each other and solve for n:

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7 0
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