The population of a city is modeled by the equation p(t) = 201,753^e0.25t where t is measured in years. if the city continues to grow at this rate, in approximately how many years will it take for the population to reach one million? (round your answer to two decimal places.)

6.40 years

Set P(t) equal to 1 million and solve for t. Logarithms make it easy.

1,000,000 = 201,753×e^(0.25t)

1,000,000/201,753 = e^(0.25t) . . . . divide by the coefficient of the exponential

ln(4.95656) = 0.25t . . . . . . take the natural log. Next, divide by the coefficient of t.

ln(4.95656)/0.25 = t ≈ 6.04

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Comment on the graph

The function graphed is the population in millions. The horizontal axis is the time in years, so the curve crosses the million mark at 6.403 years.

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0

i just took the test, the correct answer is .. 31.5 in.