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.

To solve this problem, you need to use the given equation for temperature as a function of time, Y = 70 + 110e^kt, where Y represents the temperature in Fahrenheit, t represents time in minutes, and k is a constant.

(a) To find the temperature of the turkey after 45 minutes, we can use the given information: The temperature after half an hour (30 minutes) is 153 Fahrenheit. We can substitute these values into the equation and solve for k.

153 = 70 + 110e^(30k)

First, subtract 70 from both sides:

83 = 110e^(30k)

Next, divide both sides by 110:

0.7545 = e^(30k)

To isolate the exponential term, we need to take the natural logarithm (ln) of both sides:

ln(0.7545) = ln(e^(30k))

The natural logarithm and exponential functions are inverse functions, so the ln and e terms will cancel out:

ln(0.7545) = 30k

Now we can solve for k:

k = ln(0.7545)/30 ≈ -0.00713

Now that we have the value of k, we can substitute it back into the original equation to find the temperature after 45 minutes:

Y = 70 + 110e^(-0.00713 * 45)
Y ≈ 108.4 Fahrenheit

Therefore, the temperature of the turkey after 45 minutes is approximately 108.4 Fahrenheit.

(b) To find when the turkey cools to 100 Fahrenheit, we can set up the equation:

100 = 70 + 110e^(kt)

Substitute the given values of Y (100) and solve for t:

100 - 70 = 110e^(kt)

30 = 110e^(kt)

Divide by 110:

0.2727 = e^(kt)

Take the natural logarithm (ln) of both sides:

ln(0.2727) = ln(e^(kt))

ln(0.2727) = kt

Now we can solve for t.

t = ln(0.2727)/k

Substitute the value of k we found in part (a):

t = ln(0.2727)/(-0.00713) ≈ 22.58 minutes

Therefore, the turkey will cool to 100 Fahrenheit in approximately 22.58 minutes.