Mathematics, 17.10.2019 17:00 hardwick744

The smiths spent 2,000 on clothes in a particular year if they increase the amount they spend on clothes by 10% each year the smiths will spend a total

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Answer from: Livi9666

They always increase their spending by 10%, so we can always take the previous year's spending and find 110% of it by multiplying by 1.10.

They start at 2,000

In 1 year, they spend 2000×1.1

In 2 years, they spend 2000×1.1×1.1

In 3 years, they spend 2000×1.1×1.1×1.1

In 4 years, they spend 2000×1.1×1.1×1.1×1.1

Because they only ask for four years, you could probably just multiply that out. But what if they asked for the 20th year? or the fiftieth? You wouldn't want to calculate that, you would want to find a pattern.

Well really, we want to keep track of repeated multiplication, which we can do by using exponents. Look carefully at the pattern:

year 1 = 2000×1.11

year 2 = 2000×1.12

year 3 = 2000×1.13

year 4 = 2000×1.14

Do you see it?

year n = 2000×1.1n

Finding patterns like this are going to be critical for geometric series

Answer from: Quest

b is the answer that makes most sense

step-by-step explanation:

Answer from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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