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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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Igoryamba

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A) 2280 and length is 12mm and width is 190mm

B) 190, 12

Step-by-step explanation:

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456*5= 2280

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5 0
3 years ago
William has 24 cans of fruit and 60 cans of vegetables that he will be putting into bags for a food drive. He wants each bag to
nataly862011 [7]

Answer:

See explanation

Step-by-step explanation:

William has 24 cans of fruit and 60 cans of vegetables that he will be putting into bags for a food drive.

Factor number 24 and 60:

24=2\cdot 12=2\cdot 2\cdot 6=2\cdot 2\cdot 2\cdot 3=2^3\cdot 3\\ \\60=2\cdot 30=2\cdot 2\cdot 15=2\cdot 2\cdot 3\cdot 5=2^2\cdot 3\cdot 5

Find the greatest common factor

GCF(24,60)=2^2\cdot 3=12

Hence, the greatest number of bags William can make is 12.

Each of these bags will have 24\div 12=2 cans of fruit and 60\div 12=5 cans of vegetables.

If he made fewer bags, 6 bags, each of these bags will have 24\div 6=4 cans of fruit and 60\div 6=10 cans of vegetables.

If he made fewer bags, 4 bags, each of these bags will have 24\div 4=6 cans of fruit and 60\div 4=15 cans of vegetables.

If he made fewer bags, 3 bags, each of these bags will have 24\div 3=8 cans of fruit and 60\div 3=20 cans of vegetables.

If he made fewer bags, 2 bags, each of these bags will have 24\div 2=12 cans of fruit and 60\div 2=30 cans of vegetables.

7 0
2 years ago
The area of the base of a rectangular prisim four and three fourths and the height of two and one third what is the volume
VikaD [51]
Data:
A_{base} = 4 \frac{3}{4} = \frac{4*4+3}{4} = \frac{16+3}{4} \to A_{base} = \frac{19}{4}

h (height) = 2 \frac{1}{3} =  \frac{3*2+1}{3} = \frac{6+1}{3} \to h (height) = \frac{7}{3}
v (volume) = ?

Formula: V =  A_{b}*h

Solving:
V = A_{b}*h
V =  \frac{19}{4} * \frac{7}{3}
V =  \frac{133}{12}
V = 11.08333....
\boxed{\boxed{V \approx 11.08}}\end{array}}\qquad\quad\checkmark
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3 years ago
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Arte-miy333 [17]
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