SOLUTION: The population of a town is modelled by the function P=6t^2+110t+4000
Where P is the population and t is the time in years since 2000.
a) What will the population be in 2020?
Question 1161300: The population of a town is modelled by the function P=6t^2+110t+4000
Where P is the population and t is the time in years since 2000.
a) What will the population be in 2020?
b) When will the population be 6000? Found 2 solutions by josgarithmetic, saw:Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website! ---------------------------------------------
a) What will the population be in 2020?
b) When will the population be 6000?
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(a)
Substitute 20 for t, and just evaluate P.
(b)
Substitute 6000 for P, and solve for t.
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You might find two "solutions" for part b. Make the choice for the one which obviously makes sense.
WHEN WILL THE POPULATION BE 6000?
You know how to start; right?
You know this can be simplified at least a little;
--------and you know what to do with this (If possible, factoirze, but otherwise there is general solution for quadratic equation.) Pick the result that makes sense!
You correctly solved for t. The negative value has no meaning here. The POSITIVE value found is the one which makes sense.
You can put this solution on YOUR website! Solution.
As the condition given
t represents time in years
P represents population
(a)Time in 2020 = 2020-2000 = 20
P = 6t^2+110t+4000
P = 6(20)^2+(110*20)+4000
Evaluate the power
P= 6*400+(110*20)+4000
Multiply the numbers
P = 2400+2200+4000
Add the numbers
P = 8600
Population will be 8600 in 2020.
(b)When the population be 6000
P = 6t^2+110t+4000
Use substitution
6000 = 6t^2+110t+4000
Move expression to the left side and change its sign
6000-6t^2-110t-4000 = 0
Subtract the terms
2000-6t^2-110t = 0
Use the commutative property to reorder the terms
-6t^2-110t+2000 = 0
Divide both sides of the equation by -2
3t^2+55t-1000 = 0
Solve the quadratic equation
ax^2+bx+c = 0 using
x = (-b±√(b²-4ac))/2a
t = (-55±√(55²-4*3*-1000))/2*3
t = (-55±√15025)/6
simplify the root
t = (-55±5√601)/6
Separate the solutions
t₁ = (-55+5√601)/6
t₂ = (-55-5√601)/6
Alternative form
t₁ = -29.59608
t₂ = 11.26275
Since negative value is not possible for the time in years
t = 11.26275
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