Question

(b) A gardener has a task of cutting the grass of a lawn with an area of 1000 m². On the first day, he cut an area of 16 m². On each successive day, he cuts an area 1.1 times the area that he cut the previous day the task is completed. Find the number of the days needed to complete the task. ​

Answer 1

Hi

21 days

Explanation:

`u_1=16\\\\u_2=16*1.1\\\\u_3=16*1.1^2\\...\\u_n=16*1.1^(n-1)\\\\\displaystyle\sum_(i=1)^(n) u_i=1000\\\\16*\sum_(i=1)^(n) 1.1^(i-1)=1000\\\\\\16*(1.1^(n)-1)/(1.1-1) =1000\\\\1.1^(n)-1=(1000*0.1)/(16) \\\\1.1^n=7.25\\\\n*ln(1.1)=ln(7.25)\\\\n=(ln(7.25))/(ln(1.1)) \\\\n=20.78478.... = > n=21\\`