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irina [24]
3 years ago
9

In 2016 the United States had a population of about 323 million people and was growing at 0.7 %. Use an explicit exponential mod

el to predict what year the U.S. population will reach 400 million people
Mathematics
1 answer:
ElenaW [278]3 years ago
5 0

Answer:

2047

Step-by-step explanation:

We are given that

Growing rate=0.7%

\frac{dp}{dt}=\frac{0.7}{100}P

\int \frac{dP}{P}=0.007\int dt

lnP=0.007t+C

Using the formula

\int \frac{dx}{x}=ln x+C

P=e^{0.007t+C}=e^{0.007t}\cdot e^C=Ae^{0.007t}

e^C=A

Initially when t=0,P=323 million

Substitute the values

323 million=A

P=323e^{0.007t}

Now, substitute P=400 million

400=323e^{0.007t}

ln\frac{400}{323}=0.007t

ln(1.2384)=0.007t

t=\frac{ln(1.2384}{0.007}

t=30.5\approx 31 Years

Year=2016+31=2047

Hence,In 2047 the U.S population will reach 400 million people.

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