O H5 points scalc7 9.4.008 nva (a) use the fact that the population was 250 mill

Question

O H5 points scalc7 9.4.008 nva (a) use the fact that the population was 250 million in 1990 (t to formulate a logistic model for the us popula rate, and t is the time in years since 1990.) P(t) (b) Determine the value of k in your model by using the fact that the 2000 was 275 million. (Round y population in (c) Use your model to predict the US population in the years 2100 and 220o. (Round your answers to the nearest p year 2100 P million year 2200 million (d) Use your model to predict the year in which the US population will exceed 350 million. Need Help? Talk to a Tutor 13 points scalc7 9.4.009. nvad one model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the p (a) write a differential equation that is satisfied by y. (use k for the constant of proportionality.)

Explanation / Answer

Solution:

By Using The Given Data

P(t) = P(0)e(kt) where t is the number of years since 1990.

Population in 1990 is given as 250 million, so P(0) = 250

Population in 2000 is given as 275 million, so P(10) = 275

275 = 250e(10k)

e^(10k) = 275/250 = 1.1

10k = ln(1.1)

10k = 0.0953101798

k = 0.00953102

So P(t) = 250e0.00953102t

Population in year

2100....P(110) = 713.279335 million

Population in year 2200....P(210) = 1.85 billion

To find the year that the population exceeds 350 million......

250e0.00953102t 350

e0.00953102t 350 / 250

0.00953102t ln(1.4)

t ln(1.4)/0.00953102

t ln(1.4)/0.00953102

t 35.30285705

According to this model, the population should exceed 350 million approximately 35.3 years after 1990,

or sometime in the year 2025.

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