A store had 150 laptops in the month of January. Every month, 20% of the laptops were sold and 10 new laptops were stocked in the store. Which recursive function best represents the number of laptops in the store f(n) after n months? f(n) = 150 − 0.8 x f(n − 1) + 10, f(0) = 150, n > 0 f(n) = 0.2 x f(n − 1) + 10, f(0) = 150, n > 0 f(n) = 0.8 x f(n − 1) + 10, f(0) = 150, n > 0 f(n) = 150 + 0.8 x f(n − 1) + 10, f(0) = 150, n > 0

Question

16-06-2017
Mathematics

contestada

A store had 150 laptops in the month of January. Every month, 20% of the laptops were sold and 10 new laptops were stocked in the store. Which recursive function best represents the number of laptops in the store f(n) after n months? f(n) = 150 − 0.8 x f(n − 1) + 10, f(0) = 150, n > 0 f(n) = 0.2 x f(n − 1) + 10, f(0) = 150, n > 0 f(n) = 0.8 x f(n − 1) + 10, f(0) = 150, n > 0 f(n) = 150 + 0.8 x f(n − 1) + 10, f(0) = 150, n > 0

Respuesta :

Otras preguntas

Which of the following is not a description of an evaluative conclusion? discusses the importance of the main points in the essay discusses the “big picture”

Which one of the following would be considered primarily a large muscle activity A. Dressing a doll B. Riding a rocking horse C. Putting a puzzle together D. D

Which of the following about abiotic factors in ecosystems is true? a. abiotic factors in healthy ecosystems are not in balance. b. abiotic factors are locate

one week Beth Bought three apples and eight pears for $14.50. The next week she bought 6 apples and four pears and paid $14. Find the cost of one apple and the

Which of the following physical features is located only in China?. A.The Himalayas. B.The Gobi Desert. C.Three Gorges. D.The Altay Mountains. . .

According to the u.s. constitution, what does the executive branch of the government do? a. it makes the laws. b. it reviews the laws. c. it interprets the l

What type of reaction occurs when reactants absorb heat energy to form products? a. endothermic b. exothermic c. acid-base d. nuclear

As Eastern European nations began to reform away from the Communist style of government, which nation initiated reforms first, under Solidarity, during the earl

Which gas causes an increase in the temperature in the stratosphere? nitrogen carbon dioxide ozone carbon oxalate

An effective way to improve your ability to communicate is to _______________________________________. a. be aware of when you are the receiver and when you ar

InesWalston InesWalston · Answer 1 · 2018-11-14T10:30:09+01:00

Answer-

[tex]\boxed{\boxed{f(n)=0.8(f(n-1))+10,\ f(0)=150,\ \ n>0}}[/tex]

Solution-

Here, n represents the number of months and f(n) represents the number of laptops in the store after n months.

As the store had 150 laptops in the month of January or at the beginning.

So [tex]f(0)=150[/tex]

Every month, 20% of the laptops were sold and 10 new laptops were stocked in the store.

As 20% of laptops were sold, so 80% were in the store.

So, after one month total number of laptops in the store,

[tex]\Rightarrow f(1)=0.8(150)+10[/tex]

[tex]\Rightarrow f(1)=0.8(f(0))+10[/tex] [tex](\because f(0)=150)[/tex]

Again after one month total number of laptops in the store,

[tex]\Rightarrow f(2)=0.8\times (0.8(150)+10)+10[/tex]

[tex]\Rightarrow f(2)=0.8(f(1))+10[/tex] [tex](\because f(1)=0.8(150)+10)[/tex]

Analyzing the pattern, the recursive function f(n) will be,

[tex]f(n)=0.8(f(n-1))+10,\ f(0)=150,\ \ n>0[/tex]

slicergiza slicergiza · Answer 2 · 2019-10-31T06:30:26+01:00

Answer:

f(n) = 0.8 × f(n -1) + 10, n > 0

Step-by-step explanation:

Given,

Original number of laptops, f(0) = 150, ( where, f(n) represents the number of laptops after n months )

∵ Every month, 20% of the laptops were sold and 10 new laptops were stocked in the store.

After 1 month,

The number of laptops, f(1) = original laptops - 20% of the original laptops + 10

= 150 - 20% of 150 + 10

= (100 - 20)% of 150 + 10

= 80% of 150 + 10

= 0.8 × f(0) + 10

Similarly, After 2 months,

The number of laptops, f(2) = 0.8 × f(1) + 10,

After 3 months, number of laptops, f(3) = 0.8 × f(2) + 10,

........ so, on

Thus, by following the pattern,

The number of laptops after n months,

f(n) = 0.8 × f(n -1) + 10, n > 0