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Vlad [161]
3 years ago
6

A 4 foot tree was planted in 2012 outside a high school. The tree grew continuously by 22% each year from that point. Find out w

hat the height of the tree was in 2020.
Mathematics
1 answer:
Brut [27]3 years ago
6 0

Answer:

The height of the tree in 2020 was of 19.63 feet.

Step-by-step explanation:

Exponential equation for growth:

The exponential equation for the growth of an amount has the following format:

H(t) = H(0)(1+r)^t

In which H(t) is the amount after t years, H(0) is the initial amount and r is the growth rate, as a decimal.

A 4 foot tree was planted in 2012 outside a high school.

This means that H(0) = 4

The tree grew continuously by 22% each year from that point.

This means that r = 0.22

Find out what the height of the tree was in 2020.

2020 is 2020 - 2012 = 8 years after 2012, so this is H(8).

H(t) = H(0)(1+r)^t

H(t) = 4(1+0.22)^t

H(4) = 4(1.22)^t

H(4) = 4(1.22)^8 = 19.63

The height of the tree in 2020 was of 19.63 feet.

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N is the set of odd natural numbers greater than 11 and less than 21. Use set notation to write the elements of N. N
S_A_V [24]

Answer:

N = {13, 15, 17, 19}

Step-by-step explanation:

The natural numbers greater than 11 and less than 21 are:

12, 13, 14, 15, 16, 17, 18, 19 and 20

Odd numbers are numbers that have remainders when divided by 2. Out of the numbers above, the numbers with remainders when divided by 2 are 13, 15, 17 and 19.

Since N is the set of odd natural numbers greater than 11 and less than 21,

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Step-by-step explanation:

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~PumpkinSpice1

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2 years ago
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Hey there!

The answer to your question is:

Graph A represents a growth.

Graph B represents a decay.

Graph C represents a growth.

I will give an explanation any way.

Graph A has a positive slope - a growth.

Graph B has a negative slope - a decay.

Graph C has a positive slope - a growth.

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Yanka [14]

Looks like the system is

\begin{cases}-2x+y+6z=1\\3x+2y+5z=16\\7x+3y-4z=11\end{cases}

We can eliminate y by taking

(3x+2y+5z)-2(-2x+y+6z)=16-2(1)

\implies3x+2y+5z+4x-2y-12z=16-2

\implies7x-7z=14

\implies x-z=2

so that z=x-2, and

(7x+3y-4z)-3(-2x+y+6z)=11-3(1)

\implies7x+3y-4z+6x-3y-18z=11-3

\implies13x-22z=8

Substitute z=x-2 into this last equation and solve for x:

13x-22(x-2)=8

\implies13x-22x+44=8

\implies-9x=-36

\implies x=4

Then

z=x-2

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Plug these values into any one of the original equation to solve for y:

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\implies-2(4)+y+6(2)=1

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Hence the solution is x = 4, y = -3, and z = 2.

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