Dont know what to put where?

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SchramDub

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Feb 15, 2010
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i have this equation that i have no idea what to do with so i am going to give you the entire problem.

Students participating in a psychology exeriment attended several lectures and were given an exam. Every month for a year after the exam, the students were retested to see how much of the maerial they remembered. The average scores for the group can be modeled by the human memory model.

f(t) = 90-15log of 10 (t+1) 0<=t<=12

the question is - what was t when the original exam was taken? what was the average score on the original exam? what was the average score after 6 months?
 
SchramDub said:
i have this equation that i have no idea what to do with so i am going to give you the entire problem.

Students participating in a psychology exeriment attended several lectures and were given an exam. Every month for a year after the exam, the students were retested to see how much of the maerial they remembered. The average scores for the group can be modeled by the human memory model.

f(t) = 90-15log of 10 (t+1) 0<=t<=12

the question is - what was t when the original exam was taken? what was the average score on the original exam? what was the average score after 6 months?
Click to expand...
What class is this - pre-calc, algebra-II?
Since you do not know where to begin - let us start with definitions:

What is f(t)?

What is t?

Why is f(t) present inthe problem?
 
its my triginometry class but this is algebra 2. and i think f(t) is something with the time.
 
SchramDub said:
The average scores for the group can be modeled by [function f].

This statement tells us what the variable f(t) represents.
Click to expand...

f(t) is a variable. It represents the study group's average test score, t years after taking the initial test.

At t gets larger (i.e., more time has elapsed), the value of f(t) changes.

f(t) goes down, over time. In other words, this average score becomes lower over time because human memory forgets stuff over time.

?
f(t) = 90 - 15log of 10 (t+1), with 0 <= t <= 12

I'm guessing that your phrase in red is supposed to mean "log base-10"
Click to expand...

\(\displaystyle f(t) = 90 - 15 \cdot log_{10}(t + 1)\)

Here's an example:

According to this "human memory model", what are the group's average scores 5 years and 10 years after the initial test?

Five years after the initial test, t = 5.

f(5) = 78.3

Ten years after the initial test, t = 10.

f(10) = 74.4

In other words, the average score was 3.9 points lower at year 10 than it was at year 5.

Do you now understand the three questions that this exercise asks? If not, then please reply with specific questions.

Cheers ~ Mark 8-)
 
i feel extremely slow lol but i do have another question...i am having issues plugging that into my calc. is there anyway you can run through the steps you took to get the answers for 5 and ten years so i know how to do it for the rest of the problems? and your help is greatly appreciated sir

i am trying to understand how to use the equation..i am using your example and am this far

f(t) = 90-15 x log-10(5+1)
f(t) = 90-15 x log-10(6)
f(t) = 75 x log-10(6)
log-10(6) = 6 ---because log10 always equals 1??
f(t) = 75 x 6??
 
SchramDub said:
f(t) = 90-15 x log-10(5+1)
f(t) = 90-15 x log-10(6)
f(t) = 75 x log-10(6)

We may not subtract 15 from 90 because the Order of Operations requires that we do multiplication before subtraction
Click to expand...

Also, I am concerned why you are typing "10 - log".

Will you please confirm that the given function f looks like this:

\(\displaystyle f(t) = 90 - 15 log_{10}(t + 1)\)

Finally, I cannot know which buttons you push on your calculator because I don't know what brand of calculator you're using.

Is it one of the Texas Instruments graphing calculators?
 
yes the equation is correct and the calculator i am using is a TI graphing calc

please help soon this assignment is due 2mrw
 
SchramDub said:
the calculator i am using is a TI graphing calc
Click to expand...

Those calculators have buttons for parentheses and base-10 logarithms, so you can enter the entire expression at once:

90 - 15 * LOG (5 + 1)

Pressing Enter should display something like 78.32773125 .

If you still have trouble evaluating f(t) this way, let me know which buttons you pressed and what the result is.
 
thank you that was very helpful

another question. how would i go about finding (t) when the left side of the equation (which is the average class score on the tests) equals 75
 
To solve for t, we need to use algebraic steps to first isolate the logarithmic term. Then switch to exponential form.

Here are the steps.

(1) Substitute the value 75 for the variable f(t), in the given equation.

\(\displaystyle 75 = 90 - 15 \cdot log_{10}(t + 1)\)

(2) Subtract 90 from both sides.

(3) Divide both sides by -15

(4) Switch to exponential form

\(\displaystyle 10^1 = t + 1\)

(5) Solve for t
 
thanks again

another question. the next question i encountered that i cannot seem to get a good grasp on is how to rewrite the function(equation) into another using properties of logs
 
SchramDub said:
how to rewrite the function(equation) into another using properties of logs
Click to expand...

We could use the change-of-base property for logarithms to redefine f(t) in terms of a natural log (i.e., in terms of a base-e log versus a base-10 log).

Otherwise, I'm not sure for what they're asking.

EG: Rewrite a base-b logarithm as a ratio of natural logarithms.

\(\displaystyle log_b(x) = \frac{ln(x)}{ln(b)}\)
 
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