Trig and Natural Logs: 1. m(t)=325e-0.01t, 2. tanx=3, then tan(pi+x)=?, 3. 22x+11=3x-

[hojin2]

1) Certain radioactive material decays in such a way that the mass remaining after tt years is given by the function

. . . . .m(t) = 325e−0.01t

where m(t)m(t) is measured in grams. How much of the mass remains after 25 years?

2) If tan⁡x=3 then tan⁡(π+x)= ____

3) Solve the following equation. If necessary, enter your answer as an expression involving natural logarithms or as a decimal approximation that is correct to at least four decimal places.

. . . . .22x + 11 = 3x − 26

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[tkhunny]

On the first: Do you understand what the formula means? What is "t? What is "m"?

 

[stapel]

1) Certain radioactive material decays in such a way that the mass remaining after t years is given by the function

. . . . .m(t) = 325e−0.01t

where m(t)m(t) is measured in grams. How much of the mass remains after 25 years?

As you have posted it, the equation above typesets as follows:

. . . . .\(\displaystyle m(t)\, =\, 325e\, -\, 0.01t\)

Is this what you meant? Or were there supposed to be an exponent character ("^") after the "e", and grouping symbols ("(" and ")") around the rest, so that the equation was really meant to be as follows?

. . . . .\(\displaystyle m(t)\, =\, 325e^{-0.01t}\)

Either way, what are your thoughts? What did you get when you plugged the given value in for the given variable in the given equation? Where are you stuck?

2) If tan⁡x=3 then tan⁡(π+x)= ____

You looked at the trig identities they gave you, and... then what? After plugging in to the relevant identity, how far did you get? Where are you stuck?

3) Solve the following equation. If necessary, enter your answer as an expression involving natural logarithms or as a decimal approximation that is correct to at least four decimal places.

. . . . .22x + 11 = 3x − 26

This is a question from pre-algebra or beginning algebra, waaaaaay before trig. What have you tried? Where are you stuck? You subtracted 3x from either side, and... then what?

Please be complete. Thank you!