"Certain learning processes may be illustrated by the graph of an equation of the form f(x) = a + b(1 – e–cx) , where a, b, and c are positive constants. Suppose a manufacturer estimates that a new employee can produce five items the first day on the job. As the employee becomes more proficient, the daily production increases until a certain maximum production is reached. Suppose that on the nth day on the job, the number f(n) of items produced is approximated by the following formula.
f(n)=3+20(1-e^-0.1n)
a) Estimate the number of items produced on the 6th day, the 26th day, the 28th day, a

Question

"Certain learning processes may be illustrated by the graph of an equation of the form f(x) = a + b(1 – e–cx) , where a, b, and c are positive constants. Suppose a manufacturer estimates that a new employee can produce five items the first day on the job. As the employee becomes more proficient, the daily production increases until a certain maximum production is reached. Suppose that on the nth day on the job, the number f(n) of items produced is approximated by the following formula.
f(n)=3+20(1-e^-0.1n)
a) Estimate the number of items produced on the 6th day, the 26th day, the 28th day, a

mathteacher1729 · Answer

All you do here is substitute n = 6, 26 , and 28 into the formula.

anonymous · Answer

i did but didn't get the answer(

mathteacher1729 · Answer

You might have to round.  Also be careful with parenthesis

$$\huge f(6 ) = 3 + 20 *\left(1 - e^{(-0.1\cdot (6))} \right)$$

mathteacher1729 · Answer

I've attached a graph of this function, made in geogebra. (an awesome program if you have never used it -- USE IT! :D )

mertsj · Answer

$$f(6)=3+20(1-e ^{-.1(6)})=12.0$$

mertsj · Answer

Is that what you got?

anonymous · Answer

ok, i got)) thank you)

mertsj · Answer

$$f(26)=3+20(1-e ^{-.1(26)})=21.5$$

anonymous · Answer

a) f(n) approaches 0, 
b) f(n) approaches 23
c) f(n) approaches 30
d)  equal to 23

mathteacher1729 · Answer

Ok so I went crazy and made a little video about this. Sorry for the sound quality. http://www.screenr.com/MoS8