Answer:
8196.83
Step-by-step explanation:
You want the quantity after 6 weeks of a value initially 5500 and growing at a continuous rate of 0.95% per day.
Where r is the growth rate in some time period, the value after t periods is ...
value = initial value × e^(rt)
Here we have an initial value of 5500, a growth rate of 0.95% = 0.0095, and a time period of 1 day. We want the value after 6 weeks, or 6·7 = 42 days.
That value is ...
value = 5500·e^(0.0095·42) = 5500·e^0.399 ≈ 8196.83
After 6 weeks, the quantity is 8196.83.
The value of quantity grows to 8196.83 at exponential rate.
What is exponential rate?
Exponential growth may be a method that will increase amount over time. It happens once the instant rate of modification (that is, the derivative) of a amount with relevancy time is proportional to the amount itself.
Main body:
Continuous growth
Where r is the growth rate in some time period, the value after t periods is value = initial value × [tex]e^{rt}[/tex]
Here we have an initial value of 5500, a growth rate of 0.95% = 0.0095, and a time period of 1 day. We want the value after 6 weeks, or 6·7 = 42 days.
That value is ...
value = 5500·e^([tex]e^{0.0095*42}[/tex]) = 5500·[tex]e^{0.399}[/tex] ≈ 8196.83
After 6 weeks, the quantity is 8196.83.
Therefore the value of quantity grows to 8196.83
To know more about exponential rate click on the link below
https://brainly.com/question/27161222
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