Respuesta :
Answer:
The value of the quantity after 5 decades is 607.54
Step-by-step explanation:
This quantity, after intervals of 2t decades, can be modeled by the following equation.
[tex]Q(t) = Q(0)e^{rt}[/tex]
In which Q(0) is the initial quantity and r is the rate it increases.
A quantity with an initial value of 510 grows exponentially at a rate of 7% every 2 decades.
This means that [tex]Q(0) = 510, r = 0.07[/tex]
So
[tex]Q(t) = 510e^{0.07t}[/tex]
What is the value of the quantity after 5 decades, to the nearest hundredth?
5 decades is 5/2 = 2.5 intervals of two decades.
So this is Q(2.5).
[tex]Q(t) = 510e^{0.07t}[/tex]
[tex]Q(2.5) = 510e^{0.07*2.5}[/tex]
[tex]Q(2.5) = 607.54[/tex]
The value of the quantity after 5 decades is 607.54
