Final answer:
To find the temperature of the water after 6 hours, you can use the exponential growth formula. The temperature will be 729°F.
Step-by-step explanation:
To find the temperature of the water after 6 hours, we can use exponential growth formula. The formula is T = T0 * e^(kt), where T is the temperature at time t, T0 is the initial temperature, e is Euler's number approximately equal to 2.71828, and k is the constant of proportionality. Rearranging the formula to solve for T, we have T = T0 * e^(k * 6). In this case, T0 is 27°F and T is 81°F, so we can substitute these values into the equation to find k.
First, let's find k by dividing both sides of the equation T = T0 * e^(k * 6) by T0: e^(k * 6) = T / T0. Now, take the natural logarithm (ln) of both sides to isolate the exponent: ln(e^(k * 6)) = ln(T / T0). Using the logarithmic property of ln(e^x) = x, we can simplify the equation to k * 6 = ln(T / T0). Finally, divide both sides of the equation by 6 to solve for k: k = ln(T / T0) / 6. Substitute the given values T = 81°F and T0 = 27°F, and solve for k. With the value of k, we can use the formula T = T0 * e^(kt) to find the temperature at 6 hours.
The correct answer is B) 729°F.