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Evgesh-ka [11]
3 years ago
7

Amir has spent the last three months saving money for a $1,400 computer in his local electronics store. So far he has saved $1,2

00. Today, he receives an email saying that all computers in the store are 25% off for one day only. If the sales tax charged at the counter is 7%, does Alex have enough money to purchase the computer today?
Mathematics
1 answer:
Fiesta28 [93]3 years ago
6 0
25% off of $1400 equal: 1400 + .25 = 350, so 1400 - 350 = 1050
So now the computer with 25 % off is $1050.
tax 7%, means 1050 + .07 = $73.50 (sales tax charge)

Total computer with 25% off plus 7% tax equal:

$1050 + 73.50 = $1,123.50

Amir has saved $1200, so he has enough money to purchase the computer.
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Click the picture that I sent you
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Answer: 1211.6585 years

<u>Step-by-step explanation:</u>

The equation for exponential growth is: P=P_oe^{kt}

  • P: final population
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  • t: time

Use the half life information to find k:

\dfrac{1}{2}P_o=P_oe^{k(800)}\\\\\\\dfrac{1}{2}=e^{800k}\qquad \rightarrow \qquad \text{divided both sides by}\ P_o\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=800k\qquad \rightarrow \qquad \text{applied ln to both sides}\\\\\\\dfrac{ln(\frac{1}{2})}{800}=k\qquad \rightarrow \qquad \text{divided both sides by 800}\\\\\\\large\boxed{-0.000867=k}

Next, input the information (65% decayed = 35% remaining) and the k-value to find your answer.

.35P_o=P_oe^{-0.000867t}\\\\\\.35=e^{-0.000867t}\\\\\\ln(.35)=-0.000867t\\\\\\\dfrac{ln(.35)}{-0.000867}=t\\\\\\\large\boxed{1211.6585=t}

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