We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
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]
Thanks for taking the time to read 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. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
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
