For this problem my equation is Y=70+110e^kt

but i keep getting it wrong any suggestions?

A roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed on a table in a room where the temperature is 75 Fahrenheit.
(a) If the temperature of the turkey is 153 Fahrenheit after half an hour, what is its temperature after 45 minutes?
Your answer is Fahrenheit.
(b) When will the trukey cool to 100 Fahrenheit?
Your answer is hours.

I disagree with your equation. At time=0,

temp=70+110=180F However this does not match the problem description. So it makes sense that it should be

temp=75+110e^kt that works at time zero.

153=75+110e^k*.5
78=110 e^.5k
.0709=e^.5k
take the ln of each side
.0709=.5k
solve for k, then put it in the equation
temp=75+110e^kt
at you have k, and time as .75, solve for temp.

b. solve for time when temp=100

To solve the given problem, which involves a temperature function, we'll need to use the given equation Y = 70 + 110e^kt. Let's break down the steps to solve each part of the problem.

(a) To find the turkey's temperature after 45 minutes:

1. We're given that the turkey's temperature after half an hour (30 minutes) is 153 Fahrenheit. Therefore, we can substitute Y = 153 and t = 30 minutes into the equation.
153 = 70 + 110e^(30k)

2. Next, let's solve for k, the constant in the equation. Subtract 70 from both sides:
153 - 70 = 110e^(30k)

3. Simplify the equation:
83 = 110e^(30k)

4. Divide both sides by 110:
83/110 = e^(30k)

5. Take the natural logarithm (ln) of both sides to isolate the exponent:
ln(83/110) = 30k

6. Solve for k by dividing both sides by 30:
k = ln(83/110) / 30

7. Now that we have the value of k, we can find the temperature after 45 minutes. Substitute t = 45 minutes into the equation:
Y = 70 + 110e^(kt)
Y = 70 + 110e^((ln(83/110) / 30) * 45)

Use a calculator to evaluate this equation and find the value of Y, which will be the temperature of the turkey after 45 minutes.

(b) To find when the turkey will cool to 100 Fahrenheit:

1. We need to set up the equation with Y = 100 and solve for t:
100 = 70 + 110e^(kt)

2. Rearrange the equation to isolate the exponent term:
30 = 110e^(kt) - 70

3. Divide both sides by 110:
30/110 = e^(kt) - 70/110

4. Simplify further:
3/11 = e^(kt) - 7/11

5. Add 7/11 to both sides:
3/11 + 7/11 = e^(kt)

6. Combine the fractions:
10/11 = e^(kt)

7. Take the natural logarithm of both sides:
ln(10/11) = kt

8. Solve for t by dividing both sides by k:
t = ln(10/11) / k

Now, substitute the value of k (found in part (a)) into this equation and evaluate it to find the value of t, which will be the time in hours when the turkey cools to 100 Fahrenheit.