Question 8 (1 point)A population of beetles are growing according to a linear growth model. The initial population(week 0) is Po=10, and the population after 5 weeks is P5=460.Find an explicit formula for the beetle population after n weeks.Pn=10+_ __*n

Accepted Solution

Answer:[tex]P_n=10+90n[/tex]Step-by-step explanation:So it said it was linear and gave us two points on that line: (0,10) and (5,460).y=mx+b is slope-intercept form where b is the y-intercept or the initial amount of beetles and m is the slope (or rate of change in population to number weeks) of the line.  Our variables (x,y) are really (n,P) here.The slope of the line can be computed using [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1) \text{ and } (x_2,y_2) \text{ are points on the line }[/tex].You can also just line up the points vertically and subtract, then put 2nd difference over first difference.Like this: (5  ,  460)-(0  ,    10)-------------- 5       450So the slope is 450/5=90.The y-intercept is where the line crosses the y-axis.  A graph crosses the y-axis when it's x value is 0.  Luckily, they give us the y-intercept which is (0,10) so b=10.  Your problem gave us this as well and was just asking for the slope of the line.Anyways the equation is y=90x+10 ory=10+90xor since we are using P and n:[tex]P_n=10+90n[/tex]