Final answer:
To find out how long it will take for Priscilla's money to double, we can use the formula for continuous compound interest. However, the provided options do not have a correct answer. Please double-check the question and options or seek clarification from your teacher.
Step-by-step explanation:
To find out how long it will take for Priscilla's money to double, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where A is the final amount, P is the principal amount (initial investment), e is Euler's number (approximately 2.71828), r is the interest rate, and t is the time (in years).
In this case, Priscilla wants her money to double, so the final amount will be $10,000 (twice the initial investment of $10,000). The interest rate is 11% (or 0.11 as a decimal), and we need to solve for t. Plugging in the values into the formula:
$10,000 = $10,000 * e^(0.11t)
Dividing both sides of the equation by $10,000 gives us:
1 = e^(0.11t)
Next, take the natural logarithm of both sides:
ln(1) = ln(e^(0.11t))
Using the property of logarithms that ln(a^b) = b * ln(a), we can simplify the equation to:
0 = 0.11t
Finally, solving for t:
t = 0
This means that it will take an infinite amount of time for Priscilla's money to double, which doesn't make sense. Therefore, we made an error in our calculations. The correct approach would be to use the formula for compound interest that is compounded annually. Let's solve that instead:
A = P * (1 + r)^t
We know that the initial investment (P) is $10,000, the interest rate (r) is 0.11, and we're solving for t, the time it will take to double the money. Plugging in the values:
$10,000 = $10,000 * (1 + 0.11)^t
Dividing both sides by $10,000 gives us:
1 = (1.11)^t
Taking the logarithm of both sides:
ln(1) = ln((1.11)^t)
Using the property of logarithms again, we can simplify the equation to:
0 = t * ln(1.11)
Dividing both sides by ln(1.11):
t = 0 / ln(1.11)
t = 0
Again, we obtained a nonsensical result of t = 0. This suggests that there is an error in the question or the options provided. Please double-check the question and options or seek clarification from your teacher.