i dont understand this word problem?

Question

the velocity of a sky diver (t) seconds after jumping is given by v(t)= 80(1-e^-0.2t) after how many seconds is the velocity 70ft/s? I dont understand im having a test tomorrow and a similar problem is going to be on it please help!

Answer 1

How to solve your problem:
(and as a former physics student, I understand!)

Set the velocity equal to 70.

70=80(1-e^.2t)

Next, divide both sides by 80

7/8 = 1-e^.2t

Add e^.2 t to both sides
7/8 + e^.2t= 1

subtract 7/8 from both sides

e^.2t=1/8

Take the ln of both sides
.2t= ln(1/8)

Divide by .2
t= ln (1/8)/.2

I hope this helps!

Answer 2

set your equation equal to 70.

80 (1 - e^0.2t) = 70

As there's an e in your problem and no need to derive or integrate, I'd divide both sides by 80, subtract 1 from both sides, take the natural log (ln) of both sides to eliminate the e, and solve.

-e^0.2t = 70/80 - 1
-e^0.2t = -10/80
e^0.2t = 1/8
ln (e^0.2t) = ln (1/8)
0.2t = ln 1 - ln 8
0.2t = -ln 8
t = -5 ln 8

Does that make sense? The time seems to be coming out negative, which I can't understand, but I can't find an error in the problem either.

Answer 3

This is plug and play!
70 = 80(1 - e^(-0.2t)) then untangle, divide both sides by 80,
So (7/8) = 1 - e^(-0.2t)subtract 1 from both sides, and multiply both sides by -1 to remove negative signs
(1/8)= e^ (-0.2t)
and take the natural log of both sides
-2.079= -0.2t
then divide both sides by the coefficient of t and voila! 10.397

Answer 4

1/4 of 28 is 7 - 7 go to the guidance office 28-7 is 21 - 21 remain - 1/3 of 21 is 7 - 7 go to the nurse 21-7 is 14 - 14 are left - 1/2 of 14 is 7 - 7 fo to the library 14-7 is 7 - 7 remain in the classroom

Answer 5

v(t)= 80(1-e^-0.2t) =70
1-e^-0.2t=7/8
e^-0.2t=1/8
-0.2t=ln 1/8
0.2t=ln 8
t=5 ln 8=10.40 sec

Answer 6

Shanny, you are smart but a bit of an idiot. The time is not negative. You have added MINUS ONE to both sides. So, the answer is MINUS E = MINUS T. If you multiply both sides by MINUS ONE, both sides become positive. And I teach English, not math! SHEEEEESH!