Hi,I have a linear model with equation p = 5.1t - 28, where p is the number of breeding pairs of birds and t is the year. I need to use algebra to find the year in which the linear model predicts the breeding pairs will exceed 500.
Any help appreciated.
Solve the equation
5.1t - 28 = 500
5.1t = 472
t = 472/5.1 = ___ years
Looks like a long wait.
I am assuming that "year zero" is the year when p = 28, and the counting starts. It is not 1 AD
Si, I'm assuming you meant the number of years it takes for the breeding pairs to exceed 500
P = 5.1t -28 = 500 Solve for t:
t = 528 / 5.1 = 103.5 or 104 yrs..
Yes. I agree with your answer.
Thanks
Sure, I can help you with that!
To find the year in which the linear model predicts the breeding pairs will exceed 500, we need to solve the equation when p is greater than 500.
The equation for your linear model is:
p = 5.1t - 28
We want to find the value of t (year) when p (breeding pairs) exceeds 500. So we can rewrite the equation as:
5.1t - 28 > 500
Now, let's solve for t.
Add 28 to both sides of the inequality:
5.1t - 28 + 28 > 500 + 28
Simplifying:
5.1t > 528
Next, divide both sides of the inequality by 5.1 to isolate t:
(5.1t) / 5.1 > 528 / 5.1
Simplifying:
t > 103.529
Therefore, according to the linear model, the breeding pairs will exceed 500 in the year after 103.529 or approximately 104.
Please note that in this type of model, you can only have whole number values for t (since it represents years). In this case, the year in which the breeding pairs will exceed 500 will be 104.
I hope this explanation was helpful! Let me know if you have any further questions.