Damon had answer, but i just want to see if you'll explain it differently...
The population of a town P(t)is modelled by the function P(t)=6t^2+110t+3000, where t is time in years. Note t=0 represents the years 2000. When will the population reach 6000?
Damon is the expert. I have no idea how to answer this question. I never learned about functions.
Damon's expertise it too expert for my knowledge and math level
thank you though Ms Sue.
just plug it in. 6t^2+110t+3000=6000, thus 6t^2+110t-3000=0 and we factor but first we divide by 2. Thus we get the equation 2(3t+100)(t-15)=0. FYI if you did not learn what just happened please study your algebra book. Anyway, x= -100/3 or 15, but it cannot be negative so t=15. Thus, 2000+15 = 2015
To find when the population will reach 6000, we need to set up an equation by equating the given population function to 6000 and solving for t.
The function P(t) is given as P(t) = 6t^2 + 110t + 3000. Setting this equal to 6000, we have:
6t^2 + 110t + 3000 = 6000
Now, we can rearrange this equation to obtain a quadratic equation in standard form by subtracting 6000 from both sides:
6t^2 + 110t + 3000 - 6000 = 0
Simplifying further, we get:
6t^2 + 110t - 3000 = 0
Now, we have a quadratic equation of the form ax^2 + bx + c = 0, where a = 6, b = 110, and c = -3000.
To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula, which is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values from our equation, we get:
t = (-110 ± √(110^2 - 4 * 6 * -3000)) / (2 * 6)
Simplifying further, we have:
t = (-110 ± √(12100 + 72000)) / 12
t = (-110 ± √84100) / 12
Now, we can take the square root of 84100, which is 290, simplified as:
t = (-110 ± 290) / 12
This gives us two possible solutions:
t = (-110 + 290) / 12 or t = (-110 - 290) / 12
Simplifying these expressions, we have:
t = 180 / 12 or t = -400 / 12
t = 15 or t = -33.33
Since time cannot be negative in this context, we discard the negative value. Therefore, the population will reach 6000 at t = 15 years.
Thus, the year will be 2000 + 15 = 2015.