Answer to Question #348444 in Calculus for mengal

Question

a) A plant grows 1.6 cm in the first week. Each week it grows by 5% more than it did the week before. Using geometric sequence find, how much it grows in the 6^th week.

b) In the year 2000 a shop sold 150 computers. Each year the shop sold 10 more computers than the year before. Show that the shop sold 220 computers in 2007.

c) How many students must be in a class to guarantee that at least two students receive the same score on the final exam if the exam is graded on a scale from 0 to 100 points?

Answer 1

a)

$$L(t)=1.6(1.05)^{t-1}$$

$$L(5)=1.6(1.05)^{5-1}=1.9448(cm)$$

$$L(6)=1.6(1.05)^{6-1}=2.0421(cm)$$

$$L(6)-L(5)=2.0421-1.9448=0.97(cm)$$

A plant grows 0.97 cm in the sixth week.

b)

$t=year-2000$

$$N(t)=150+10t$$

$2007: t=7$

$$N(7)=150+10(7)=220$$

c) There are $1+100=101$ possible different scores.

Then  by the pidgeon hole principle, you must have 102 students in class to assure that two of them get the same score.