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KiRa [710]
3 years ago
12

Mohamed decided to track the number of leaves on the tree in his backyard each year. the first year, there were 500500500 leaves

. each year thereafter, the number of leaves was 40\%40%40, percent more than the year before. let f(n)f(n)f, left parenthesis, n, right parenthesis be the number of leaves on the tree in mohamed's backyard in the n^\text{th}n th n, start superscript, t, h, end superscript year since he started tracking it. fff is a sequence. what kind of sequence is it
Mathematics
2 answers:
VARVARA [1.3K]3 years ago
8 0

Mohamed decided to track the number of leaves on the tree in his backyard each year. the first year, there were 500 leaves. each year thereafter, the number of leaves was 40% more than the year before. let f(n) be the number of leaves on the tree in Mohamed's backyard in the n^th year since he started tracking it. f is a sequence. what kind of sequence is it?

Number of leaves on the tree in first year = 500

The number of leaves was 40% more than the year before.

So rate of increase is 40/100 = 0.4

We use exponential growth formula,

f(n) = a(1+r)^n

Where a is the initial number, r is the rate of growth, n is the number of years

We know a= 500, r= 0.4

f(n) = 500(1+0.4)^n

f(n) = 500(1.4)^n

Plug in n=1,2,3...

f(1) = 500

f(2) = 500 * 1.4^1

f(3) = 500 * 1.4^2 and so on

From this we can see that the common ratio is 1.4

Hence it is a Geometric sequence.

Gnom [1K]3 years ago
6 0

Answer:

1. geometric sequence 2.f(1)=500

f(n)=f(n−1)⋅1.4

Step-by-step explanation:

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Answer:

See Below.

Step-by-step explanation:

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We can see that her bank balance first reached $400 on Day 4 and continued until Day 8.

Part A)

Since the maximum amount is $400, it is whenever the graph reaches (and stays) at its maximum, or the highest points on the graph.

We can see that at around Day 4, she first reached her maximum of $400 since that is the highest point of the graph.

And this continues until approximately Day 8.

Therefore, Ebony first reached $400 on Day 4 and stayed at $400 until Day 8.

Part B)

Refer above. The explanation is the same.

Part C)

Jade is says that the amount Ebony is depositing per day from Days 0 to 4 is the same as the amount Ebony is withdrawing per day from Days 8 to 12.

We also know that Day 12 is when Ebony’s account first reached 0.

Essentially, Jade is saying that the <em>slope</em> of the line from Days 0 to 4 is <em>the same</em> as the <em>slope</em> of the line from Days 8 to 12.

Ignoring the negative, we can immediately see that this is not true without calculating.

This is because the slope of the line from Days 8 to 12 is much steeper than than slope of the line from Days 0 to 4.

So, the two slopes are not equal since they are not the same steepness.

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3 years ago
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One integer is 3 less than another. The sum of their square is 317. Find the integers
sergij07 [2.7K]
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3 years ago
Given the equation 4x + 7 = 3(2x − 5), solve for the variable. Explain each step and justify your process. B. Sam solved a simil
arlik [135]
Equation: 4x + 7 = 3(2x - 5)

Step-by-step solution:

• Expand brackets

-> 4x + 7 = 6x - 15

• Move x variable to a side and the numbers to another

-> 4x - 6x = -15 - 7

• Solve

-> -2x = -22

• Multiply both sides by (-1)

-> -(-2x) = -(-22)
-> 2x = 22

• Divide both sides by 2

-> x = 22/2

-> x = 11

• Justification
-> Put x = 11 in original equation
-> 4(11) + 7 = 3( 2(11) - 5)
-> 44 + 7 = 3(22 - 5)
-> 51 = 3(17)
-> 51 = 51
-> 51 - 51 = 0
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Step-by-step explanation:

4 0
3 years ago
B2-4b+4=0 using quadratic forumla
Ivan

Trying to factor by splitting the middle term   

Factoring <span> b2-4b+4</span> 
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The middle term is, <span> -4b </span> its coefficient is <span> -4 </span>.
The last term, "the constant", is <span> +4 </span>

Step-1 : Multiply the coefficient of the first term by the constant <span>  1 • 4 = 4</span> 

Step-2 : Find two factors of  4  whose sum equals the coefficient of the middle term, which is  <span> -4 </span>.
<span><span>     </span></span>

<span><span>-4   +   -1   =   -5</span><span>     -2   +   -2   =   -4   That's it</span></span>


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  -2 
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Step-4 : Add up the first 2 terms, pulling out like factors :
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              Add up the last 2 terms, pulling out common factors :
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Step-5 : Add up the four terms of step 4 :
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3 years ago
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