Problem

Solve each problem. A seating section in a theate…

04:19

Problem 44 Hard Difficulty

Solve each problem.
Repeat Exercise $43,$ but assume that the starting salary is $\$ 2000$ per month and the guaranteed increase is $\$ 100$ every four months for 3 yr.

Answer

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Precalculus

Beginning and Intermediate Algebra

Chapter 14

Sequences and Series

Section 2

Arithmetic Sequences

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Video Transcript

Now we're told that this question is very similar to the last. Except in this case, we're told that the starting salary is $2000 and they're going to get a raise of $100 every four months for three years. So we want to know what's going to be their salary at the end of this time. So let's think of this like a sequence. Well, because we're looking for the salary in three years, not the total that they've made. That means we're trying to find a sev ent. We're trying to find the particular terms in the sequence while we know that they're starting off with $2000. So then four months later, they're gonna make an extra $100 so they'll be making $2100. Well, not $21,000 about person would really like it if it was that Well, four months later, which is really means at the end of eight months, let's spell this right. So this means after eight months they're gonna make enough $400 so there are up to 2200. Then if we tack on another four months, which if you think about it. That's after a full year. They're gonna Salary will increase by another $100 which means their salary will be 2300. Well, let's think about this. Pattern is going to continue. So every year was C increase is going to increase by $300 per year. So how much are they going to make at the end of the second year? Well, we're gonna add 300. So that would be 2600 in Let's make that ledge all bull here. 2600. So again, so Afghans of three years, they're gonna make an additional $300. So 2900. So perfect. Now we found that the ends of three years, they will be making $2900 a month.

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