Okay, so
I worked out
17 = T(10) = 2 + 23e ^10k
15/23 = e^10k
k= 1/10ln(15/23)
k = - 0.043
But when I do this equation
17 = T(30) = 2 + 23e^30k
15/23 = e^30k
k = 1/30ln(15/23)
k = -0.142
But the answer is apparently 8.38?
Can someone please help.
I think I'm getting too tired and I can't pick up on my mistakes. =(
well of course if
T(t) = 2+23e^kt
T(10) will not equal T(30)
You sure they're both supposed to be 17?
So, what was the original problem?
Suppose that the temperature of the environment is 2 degrees and the initial temperature of the object is 25 degrees. After 10 minutes the temperature of the object is observed to be 17 degrees.
what is the temperature of the object after 30 minutes?
after how many minutes is the temperature of the object 4 degrees?
As I recall, you need Newton's law of cooling, which in this case would be
T(t) = 2+23e^(-kt)
where we try use a positive k.
T(10) = 17, so
2+23e^(-10k) = 17
k = 0.0427
and we have T(t) = 2+23e^(-.0427t)
So, after 30 minutes,
T(30) = 2+23e^(-.0427*30) = 8.388
When T=4, we have
2+23e^(-.0427t) = 4
t = 57.20
Ahhhhh! Okay awesome! Thank you!
Makes so much sense!
I see that you're working with an equation involving exponential functions and trying to solve for the value of k. It seems like you're using the equation T(t) = 2 + 23 * e^(kt), where T(t) represents a function that depends on time t.
To find the value of k in the equation T(10) = 2 + 23 * e^(10k), you correctly set up the equation and solved for k. You found k = 1/10 * ln(15/23), which is approximately -0.043.
Now, to solve for k in T(30) = 2 + 23 * e^(30k), you followed a similar approach. However, the value you obtained for k is different from what you expected.
To understand the issue, let's go through the process step by step:
1. Start with the equation T(30) = 2 + 23 * e^(30k).
2. Divide both sides of the equation by 23 to isolate the exponential term: (T(30) - 2) / 23 = e^(30k).
3. Take the natural logarithm (ln) of both sides of the equation to eliminate the exponential term: ln((T(30) - 2) / 23) = 30k.
4. Now, divide both sides of the equation by 30 to solve for k: k = (1/30) * ln((T(30) - 2) / 23).
It seems like you made an error when dividing by 30, which is causing the discrepancy in the result. Make sure to divide by 30 instead of 1/30 when applying this step.
Once you recalculate using the correct value of k, you should be able to find the answer for T(30). If you provide the value of T(30), I can assist you further in obtaining the accurate value of k.