Answer to Question #121412 in Algebra for queen

Question

A new annual festival just began in a small town in northern Alberta. In the first year, the festival had 25 participants. It is expected that the number of people attending the festival will double every year.

In how many years can the organizers expect 800 people in attendance?

Answer 1

Explanations & Calculations

• If we write the expected sequence of the number of expected participants,

25,50,100,200.....

• $\frac{50}{25}=\frac{100}{50}=\frac{200}{100} =\small 2$
• Therefore, the above sequence lays on a geometrical progression with common ration (r =) 2.

• So it's possible to write : Participants = 25$\times$(2)^n-1 ; n being the year in consideration

• Therefore,

$\qquad\qquad \begin{aligned} \small 800 &= \small 25\times2^{n-1}\\ \small 2^{n-1} &= \small 32\\ &= \small 2^5\\ \small n-1 &= \small 5\\ \small n &= \small 6 \end{aligned}$

• Therefore, 800 participants could be expected in another 5 years .(on 6^th year from the start)