After how many seconds is their velocity 70 ft/s?

Question

The velocity of a sky diver t seconds after jumping is given by v(t) = 80(1 − e^−0.02t), measured in feet
per second. 

Answer 1

70 = 80 ( 1 - exp(-0.02t))

 

7/8 = 1 - exp(-0.02t)

 

-1/8 = -exp(-0.02tt)

 

1/8 = exp(-0.02t)

 

ln(1/8) = -0.02t

 

ln(1) - ln(8) = -0.02t

 

-ln(8) = -0.02t

 

ln(8)  = 0.02t

 

t = ln(8)/ 0.02 = ln(8)/ {2/100}

 

       = 100*ln(8)/2 = 50 * ln(8) 

 

    approximately 104