Final answer:
The value of the quantity after 1.25 days, to the nearest hundredth, is 7430.09.
Explanation:
To find the value of the quantity after 1.25 days, we need to use the formula for continuous decay, which is given by Q(t) = Q0 * e^(rt). Here, Q(t) represents the quantity at time t, Q0 represents the initial quantity, r represents the decay rate, and e is the base of the natural logarithm.
In this problem, we are given that the initial value is 7800 and the decay rate is 0.1% per hour. We need to find the quantity after 1.25 days, which is equivalent to 30 hours. So, plugging in the values in the formula, we get Q(30) = 7800 * e^(0.001 * 30) = 7800 * e^0.03.
To calculate the final answer, we need to use a calculator or a mathematical software. Using a calculator, we get the value of e^0.03 as 1.03045. Multiplying this by 7800, we get the final answer as 7430.09.
Explanation continued: Now, let’s break down the calculation to understand how we arrived at the final answer. Firstly, we found the value of e^0.03, which is equivalent to 1.03045. This means that the quantity decays by 1.03045 times every hour. To find the quantity after 30 hours, we multiply the initial quantity by this factor 30 times. This is equivalent to finding 7800 * 1.03045 * 1.03045 * … * 1.03045 (30 times). This can also be written in the form of an exponent, which is 7800 * (1.03045)^30.
Simplifying this, we get 7800 * 1.03045^30 = 7430.09. This final answer is rounded to the nearest hundredth, as required in the question.
In conclusion, we can see that the quantity decays continuously by a small amount every hour, but over a period of 1.25 days, the overall reduction in the quantity is significant. This problem highlights the importance of understanding continuous decay in real-life scenarios, where certain products or substances may lose their value over time.