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nordsb [41]
3 years ago
13

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 quantit

y after 186 hours to the nearest hundredth
Mathematics
2 answers:
Soloha48 [4]3 years ago
3 0

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


lara [203]3 years ago
3 0

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

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