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 back yard in the n^\text{th}n th n, start superscript, start text, t, h, end text, end superscript year since he started tracking it. fff is a sequence. What kind of sequen

2 answers

Question:

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 back yard in the n^\text{th}n th n, start superscript, start text, t, h, end text, end superscript year since he started tracking it. fff is a sequence. What kind of sequence is it?

Answer:[tex]f(n) = (1.4)^{(n - 1)} \times 500[/tex]The sequence is a geometric sequence.Step-by-step explanation:The number of leaves in the tree in the first year is 500.And the number of leaves in the tree in the second year increases by 40% of the number in the first year.So, it will be [tex]500(1 + \frac{40}{100}) = 1.4 \times 500[/tex]Again, the number of leaves in the tree in the third year increases by 40% of the number in the second year and so on.Therefore, the number of leaves in the tree in the third year will be [tex]1.4 \times 500 \times (1 + \frac{40}{100}) = (1.4)^{2} \times 500[/tex] and so on.If we want to calculate the number of leaves in the tree in the nth year by f(n) then it will be given by [tex]f(n) = (1.4)^{(n - 1)} \times 500[/tex] Therefore, the sequence is a geometric sequence. (Answer)

answer from rani01654

2

Answers #2

Answer:Geometric sequencef(1)= 500
f(n)=f(n-1) x 1.4Step-by-step explanation:

Which is the government agency that covers customer deposits if a bank fails?the central bankthe member bankthe Federal Deposit Insurance Corporation (FDIC)the Federal Reserve System...

The molecular weight of NaCl is 58.44 grams/mole. If you had a 1.0 molar solution (1.0 M), you would have to put 58.44 g of salt in 1.0 liter of solution.
How many moles of NaCl would you have in 100 mL of this solution?
a. 0.010
b. 0.10
c. 0.58
d. 5.8...

Which of the following BEST explains why President Lyndon Johnson, subsequent to President Kennedy’s assassination, did not have the support of a vice president? A. His vice president proved to be too inexperienced to perform his duties. B. His vice president had to resign immediately due to alleg...

Which of the following was formed mainly in response to disagreements over the extent of the federal government's power? A: Taxation without representationB: Territorial expansion westC: Judicial reviewD: Creation of political parties...

a customer buys $12.42 in merchandise and gives the cashier a ten dollar bill, a five dollar bill, a dime, a nickel and two pennies. her correct change is:...