Question

You can model the population of a certain city between the years 1965 and 1995 by the radical function P(x) = 75,000 ^3sqrt x-1940. Using this model, in what year was the population of that city 245,000
A.1973
B.1975
C.1979
D.1970

Answer 1

Answer: B. 1975

Step-by-step explanation:

Given:  The model of population of a certain city between the years 1965 and 1995 by the radical function

$P(x)=75000\sqrt[3]{x-1940}$

To find the x year at which population is 245,000, put this in equation we get

$245000=75000\sqrt[3]{x-1940}\\\\\Rightarrow\frac{245000}{17000}=\sqrt[3]{x-1940}\\\\\Rightarrow3.266=\sqrt[3]{x-1940}\\\\\Rightarrow\ x-1940=(3.266)^3..........\text{[by taking cube on both sides]}\\\\\Rightarrow\ x-1940=34.8587\\\\\Rightarrow\ x=1940+34.8587\\\\\Rightarrow\ x=1974.8587\approx1975$

Hence, at year 1975 the population of the city is 245,000.

Answer 2

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 If P(x) = 245000... 

245000 = 75000(x - 1940)^(1/3) 
x ≈ 1975