in 1900, greenville had a population of 4000 people. Greenville's population increased by 100 people each year. Springfield had a population of 1000 people. Springfields population increased bu 4% each year. In what year were the populations about equal?

Question

Mathematics

Krish

1 May, 17:56

in 1900, greenville had a population of 4000 people. Greenville's population increased by 100 people each year. Springfield had a population of 1000 people. Springfields population increased bu 4% each year. In what year were the populations about equal?

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Answers (1)

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Khalil Pham · Answer 1

Answer: year 1948

Step-by-step explanation:

1900 is our t = 0

The population of Greenville can be written as:

G = 4000 + 100*t

the equation for Springfield can be written as:

S = 1000 * (1.04) ^t

we want to find the value of t that makes S (t) = G (t)

4000 + 100*t = 1000 * (1.04) ^t

(4000 + 100*t) = 1.04^t

4 + 0.1*t = 1.04^t

now, you can graph both of this equations (left side and right side) and see in wich value of t the graphs intersect eachother, or you also may use different values of t until the values are about the same for both sides, which is the thing i did with the equation:

4 = 1.04^t - 0.1*t

You will find that the correct value is t = 48

So we can assume that in year 1948 the populations will be about the same.