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zaharov [31]
3 years ago
13

The housing market in Dallas, Texas, experienced a 9.8% increase in the past year. If the median home price was $96,812 one year

ago, what is the current median home price? Round your answer to the nearest dollar.
Mathematics
1 answer:
JulijaS [17]3 years ago
5 0

Answer:  $106,300

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

A = P(1 + r)

  • A is the accrued amount (balance)
  • P is the principal (initial amount)
  • r is the rate --> convert to a decimal

Given: P = 96,812    r = 9.8% --> 0.098

A = 96,812(1 + 0.098)

   = 96,812(1.098)

   = 106,299.576

rounded to the nearest dollar is $106,300

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4 years ago
One model for the spread of a virusis that the rate of spread is proportional to the product of the fraction of the population P
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Answer:

The differential equation for the model is

\frac{dP}{dt}=kP(1-P)

The model for P is

P(t)=\frac{1}{1-0.99e^{t/447}}

At half day of the 4th day (t=4.488), the population infected reaches 90,000.

Step-by-step explanation:

We can write the rate of spread of the virus as:

\frac{dP}{dt}=kP(1-P)

We know that P(0)=100 and P(3)=100+200=300.

We have to calculate t so that P(t)=0.9*100,000=90,000.

Solving the diferential equation

\frac{dP}{dt}=kP(1-P)\\\\ \int \frac{dP}{P-P^2} =k\int dt\\\\-ln(1-\frac{1}{P})+C_1=kt\\\\1-\frac{1}{P}=Ce^{-kt}\\\\\frac{1}{P}=1-Ce^{-kt}\\\\P=\frac{1}{1-Ce^{-kt}}

P(0)=  \frac{1}{1-Ce^{-kt}}=\frac{1}{1-C}=100\\\\1-C=0.01\\\\C=0.99\\\\\\P(3)=  \frac{1}{1-0.99e^{-3k}}=300\\\\1-0.99e^{-3k}=\frac{1}{300}=0.99e^{-3k}=1-1/300=0.997\\\\e^{-3k}=0.997/0.99=1.007\\\\-3k=ln(1.007)=0.007\\\\k=-0.007/3=-0.00224=-1/447

Then the model for the population infected at time t is:

P(t)=\frac{1}{1-0.99e^{t/447}}

Now, we can calculate t for P(t)=90,000

P(t)=\frac{1}{1-0.99e^{t/447}}=90,000\\\\1-0.99e^{t/447}=1/90,000 \\\\0.99e^{t/447}=1-1/90,000=0.999988889\\\\e^{t/447}=1.010089787\\\\ t/447=ln(1.010089787)\\\\t=447ln(1.010089787)=447*0.010039225=4.487533

At half day of the 4th day (t=4.488), the population infected reaches 90,000.

8 0
3 years ago
Janelle has d dimes and n nickels. Her sister has 5 times as many times and 6 times as many nickels as Janelle has. Write the su
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Answer:

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If Janelle has dimes and nickels, she has d + n. If her sister has 5 times the number of dimes, she has 5d; if her sister has 6 times the number of nickels she has 6n.

d + n + 5d + 6n --> 6d + 7n

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