Question

The temperature, F, in degrees Fahrenheit, after t hours of a roast put into an oven is given by the equation F=325-185e^-0.4t. What was the temperature of the roast when it was put into the oven?
(1) 325
(2) 200
(3) 185
(4) 2018
Please help me out

Answer 1

Answer:

1) 325° F

Step-by-step explanation:

To find the temperature of the roast when it was put into the oven, we need to use the given equation:

$F = 325 - 185e^{-0.4t}$
In oven cook well done allow 25-30 minutes per 500g of meat, so, time (t) = 30 minutes.
Now
Substitute $t = 30$ into the equation:

$F = 325 - 185e^{-0.4 \times 30}$

Now, let's calculate the value of $e^{-0.4 \times 30}$:

$e^{-0.4 \times 30} = e^{-12}$

Now, compute the value of $e^{-12}$:

$e^{-12} \approx 6.14421235 \times 10^{-6}$

Now, substitute the value of $e^{-12}$ back into the equation:

$F = 325 - 185 \times 6.14421235 \times 10^{-6}$

$F = 325 - 0.001136679285$

$F \approx 324.9988633$
$F \approx 325 \textsf{(in nearest whole number)}$

So, the temperature of the roast when it was put into the oven was:

1) 325 °F