Question

a quantity with an initial value of 2100 decades exponentially at a rate of 0.65% every 10 days what is the value of the quantity after 186 hours to the nearest hundredth

Answer 1

Answer:

The value of the quantity after 186 hours is 2089.41

Step-by-step explanation:

We can use exponential formula

$P(t)=a(1-b)^{\frac{t}{h} }$

a quantity with an initial value of 2100

so,

$a=2100$

decays exponentially at a rate of 0.65% every 10 days

So, b=0.0065 when h=10*24=240

now, we can plug values

$P(t)=2100(1-0.0065)^{\frac{t}{240} }$

now, we can plug t=186

and we get

$P(186)=2100(1-0.0065)^{\frac{186}{240} }$

$=2089.413$

Answer 2

Answer:

Q(186)  = 2089.463                    

Step-by-step explanation:

Formula for decaying exponentially:

Q(t) = Q_0 e^{-rt}

where, Q(t)= quantity at time t

Q_0 = initial quantity value (2100)

t = time (186 hours)

r = rate of decaying (0.65)

r = 0.65% = 10 days

1 day = $\frac{0.0065}{10}$

1 hour = $\frac{0.0065}{240}$

186 hours = $\frac{0.0065*186}{240}$

rt = 0.00503

Q(186) = 2100*e^{-0.00503}

          = 2089.46