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an average student enrolled in a typing progressed at a rate of words per minute t weeks after enrolling in a 15-week course. if a student could type 25 words per minute at the beginning of the course, that is , find: a) how many words per minute, n(t), would the student be expected to type after t weeks into the course?

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Let's say that an average student's typing speed increases by a certain number of words per minute every week. Let's call this rate of increase "r" words per minute per week. So, every week, the student types "r" words faster than the previous week.

We can write a formula for the student's typing speed, n(t), as a function of the number of weeks, t, after enrolling in the course:

n(t) = initial typing speed + (rate of increase * number of weeks)

= 25 + r * t

Now, let's dissect this formula:

1. 25 represents the initial typing speed in words per minute, which is given.

2. r is the rate at which the typing speed increases every week, in words per minute per week.

3. t is the number of weeks since the beginning of the course.

Imagine if r were 2. This would mean the student types 2 words per minute faster each week. After one week, t = 1, the student would type:

n(1) = 25 + 2*1

= 25 + 2

= 27 words per minute

After two weeks, t = 2, the student would type:

n(2) = 25 + 2*2

= 25 + 4

= 29 words per minute

And so on.

Unfortunately, we don't know the value of "r" from the information provided. If the problem gave us more information, such as how fast the student types at the end of the course, we could use that to find "r" and make specific predictions.

However, without knowing "r", the formula n(t) = 25 + r*t gives you a general idea of how the typing speed changes over time.

That's it! It’s like baking a cake. The initial typing speed is the plain cake, and every week you’re adding some frosting (increase in typing speed) to make it better and tastier (faster). The “r” tells you how much frosting you're adding each week!

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