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

Answer 1

Hello there!

v(t) = 80(1-e^0.02t)

Plug in 70 ft/s to the v(t)

70 ft/s = 80(1-e^0.02t)

70 ft/s = 80 - 80e^0.02t

-10 ft/s = -80e^0.02t

10 ft/s = 80e^0.02t

1/8 ft/s = e^0.02t

ln(1/8) = ln(e^0.02t)

ln(1/8) = t

0.02

Plug into calculator!

t = 103.97 seconds. (approximately)

Hope this helps!