Question

Question: You are playing your favorite video game, Hero's Quest. In the game, you can complete missions to earn experience points. You may complete a mission as many times as you would like, but each time you do, you only receive 80% as much experience as the previous time. The first time that you complete Mission A, you earn 1000 experience, points. The second time you complete it, you earn 800 experience points. How many times can you complete the mission before you earn less than 400 points? Explain your answer​

Answer 1

Using a geometric sequence, it is found that you can complete the mission 5 times before you earn less than 400 points.

What is a geometric sequence?

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

$a_n = a_1q^{n-1}$

In which $a_1$ is the first term.

In this problem, the amount of points after n times is a geometric sequence with $a_1 = 1000, q = 0.8$, hence the equation is:

$a_n = 1000(0.8)^{n-1}$

You will earn less than 400 points when:

$a_n < 400$

Hence:

$1000(0.8)^{n-1} < 400$

$(0.8)^{n-1} < 0.4$

$\frac{0.8^n}{0.8} < 0.4$

$0.8^n < 0.32$

$\log{0.8^n} < \log{0.32}$

$n > \frac{\log{0.32}}{\log{0.8}}$

$n > 5.1$

You can complete the mission 5 times before you earn less than 400 points.

More can be learned about geometric sequences at https://brainly.com/question/11847927