A population of beetles are growing according to a linear growth model. The initial population (week 0) is P
0
=
5
, and the population after 7 weeks is
P
7
=
47
.
After how many weeks will the beetle population reach 113?

9514 1404 393

  18 weeks

Step-by-step explanation:

We are given the (time, population) pairs (0, 5) and (7, 47). With these values, we can use the two-point form of the equation of a line to write the equation of the linear model.

  p = (p2 -p1)/(t2 -t1)(t -t1) +p1

  p = (47 -5)/(7 -0)(t -0) +5

  p = 6t +5 . . . . . the linear model matching the given points.

For p = 113, the time (number of weeks) is ...

  113 = 6t +5

  108 = 6t . . . . . . subtract 5

  18 = t . . . . . . . . . divide by 6

After 18 weeks, the beetle population will reach 113.