Question

boat is pushed to water. it moves distance s in time t with formula:
s = 25m*(1-e^-(k*t))
where k is boat constant. when time is 6s boat has moved 10m. what is distance after 26 seconds?

I don't know how to remove exponent. can someone help me to right direction? :/

10m = 25*(1 - e^-(k*6)) //:25
0.4 = 1 - e^-(k*6) // -1
-0.6 = e^-(k*6)
ln(k*6) = ln(0.6)

so something is wrong.

Answer 1

Your last step isn't right. You also dropped a negative.
\[-0.6 = -e ^{-(6k)}\]
Multiply it all by -1, then taking logs of both sides yields
\[\ln 0.6 = {-(6k)}\]


This is the log property you messed up on:
\[\ln e^x = x ln e = x\]
but you had done it as \[\ln e^x = \ln x\]

Answer 2

so
ln(0.6)\[k = \frac{ \ln(0.6) }{ 6 } = -0.085137603\]

i think that's right. thanks :)

Answer 3

Almost, but you dropped a negative again.

\[\ln 0.6 = {-(6k)} \]
\[k = \frac{ - \ln 0.6 }{ 6 }\]
So your answer should be +0.0851