Chapter 11.5, Problem 48PPS

To determine

Find when she will kill the monster.

Answer to Problem 48PPS

The monster will be killed after $260$ seconds.

Explanation of Solution

Given:

The final monster in Helena`s video game has 100 health points. During the final battle, the monster regains 10 % of its health points after every 10 seconds. If Helena can inflict damage to the monster that takes away 10 health points every 10 seconds without getting hurt herself, will she ever kill the monster? If so, when?

Concept Used:

Starting at 100 HP, the monster would take 10 HP damage so it will have 90 HP but also regains 10% of the current HP, so we multiply the difference by 1.1.

Thus pattern continues until the monster is defeated where its HP drops to 0.

The final monster`s current health can be modeled by the recursive formula: $a_n=1.1(a_{n-1}-10);a_1=100$

Calculation:

Starting at 100 HP, the monster would take 10 HP damage so it will have 90 HP but also regains 10% of the current HP, so we multiply the difference by 1.1.

Thus pattern continues until the monster is defeated where its HP drops to 0.

The final monster`s current health can be modeled by the recursive formula: $a_n=1.1(a_{n-1}-10);a_1=100$

Using graphing calculator enter 100

Input $\left(\text{ANS }–10\right)·1.1$ and note how many of ENTER until the result is less than 0. After 26 presses, the result is less than 0 so the monster will be killed after $26·10=260$ seconds.

So the monster will be killed after $260$ seconds.

Thus, the monster will be killed after $260$ seconds.