The answer to this should be 201.7, but I keep getting off track.
300=70+(375-70) e^ -k*10
230=305 e^-10*k
ln 230=ln 305 e^-10*k
ln 230= ln 305 -10*k
yes, you do get off track.
Line 3 should be
(because ln ab = ln a + ln b)
ln 230=ln 305 + ln( e^-10*k)
ln 230 - ln 305 = -10k
because ln(e^x) = x
now go from there.
In fact, I'd have divided first:
230=305 e^-10*k
230/305 = e^-10k
201.7? I get nothing like that
.75 = e^-10k
-10k = -.287
k = .0287
There must be something wrong with the way you wrote the problem.
I mean e^(-10*201.7) = a very very very tiny number. Some missing parentheses?
To solve this equation and find the value of k, you can follow these steps:
Step 1: Start with the equation:
ln(230) = ln(305) - 10k
Step 2: Rewrite the equation by moving ln(305) to the other side:
ln(230) + 10k = ln(305)
Step 3: Subtract ln(230) from both sides to isolate 10k:
10k = ln(305) - ln(230)
Step 4: Use a calculator to find the values of ln(305) and ln(230):
ln(305) ≈ 5.7203
ln(230) ≈ 5.4381
Step 5: Substitute the values into the equation:
10k = 5.7203 - 5.4381
Step 6: Subtract the values to solve for k:
10k ≈ 0.2822
Step 7: Divide by 10 to find the value of k:
k ≈ 0.2822 / 10
Step 8: Simplify the division to get the final value of k:
k ≈ 0.0282
Now that you have found the value of k, you can substitute it back into the original equation and solve for the missing variable.