S(t) = 68 − 20 log (t + 1), t ≥ 0 What was the average score after 4 months? after 24 months? After what time t was the average score 50%?

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S(t) = 68 − 20 log (t + 1), t ≥ 0 What was the average score after 4 months? after 24 months? After what time t was the average score 50%?

Mathematics
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Round to the nearst two decimal places
calculator exercise. replace t by 4, and 24. i will write it if you like

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is this log base ten?
i dont get it
t = time in months yes?
so for the first one put \[S(4)=68-20log(4+1)=68-20log(5)\]
in other words put 4 where you see a t and then compute
you need a calculator to find log(5)
i got 54.02
let me try
\[S(24)=68-20log(25)=...\]
i let me know if you have an answer
okay me to so for 24 months its 40.04
sound right
hold on i will compute
yup that is what i got
now we have to find when S = 50. do you know how to do that one?
no
first replace S(t) by 50 \[50=68-20log(t+1)\] then get the log by itself on one side \[20log(t+1)=68-50=18\]
ok so far?
no , why did you put 68-50
ok let me go step by step. \[50=68-20log(t+1)\] add \[20log(t+1)\] to both sides to get \[20log(t+1)+50=68\] then subtract 50 from both sides to get \[20log(t+1) = 68-50=18\] then divide by 20 to get \[log(t+1)=\frac{18}{20}=\frac{9}{10}=.9\]
i did not need to add log(t+1) to both sides, but i prefer dealing with positive things when i am trying to solve. i could have subtracted 68 from both sides and gotten the same answer working with negative numbers. matter of preference.
so we have arrived via some algebra at \[log(t+1)=.9\] is that ok so far?
yes i think im getting it
these were just algebra steps to get log(t+1) by itself. same steps i would have used to solve for x if the equation was \[50=68-20x\]
you would get \[x=.9\] and here \[x=log(t+1)\] so \[log(t+1)=.9\]
we are not done yet, though because we have to solve for t.
okay im following you
\[log(x)=y \] \[10^y=x\]
what i meant to say was \[log(x)=y\] means the same thing as \[10^y=x \]
here we have \[log(t+1)=.9\] so \[10^{.9}=t+1\]
to find \[10^{.9}\] in need a calculator. then to get t by itself subtract 1.
let me know what you get.
6.94 sound right
its wrong???

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