Question

A quantity with an initial value of 510 grows exponentially at a rate of 7% every 2 decades. What is the value of the quantity after 5 decades, to the nearest hundredth?

Answer 1

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.

$Q(t) = Q(0)e^{rt}$

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 $Q(0) = 510, r = 0.07$

So

$Q(t) = 510e^{0.07t}$

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).

$Q(t) = 510e^{0.07t}$

$Q(2.5) = 510e^{0.07*2.5}$

$Q(2.5) = 607.54$

The value of the quantity after 5 decades is 607.54