Question

A population of beetles are growing according to a linear growth model. The initial population (week 0) is p0=6 and the population after 7 weeks is p7=83 find an explicit formula for the beetle population after n weeks.

Answer 1

Answer:

11n + 6

Step-by-step explanation:

As its a linear equation hence

y = mx  + c  would be the Equation

y = p  = Population

x  = w  = Number of weeks

p  = mw  + c

p(w) = mw + c

for w = 0  , p = 6

p(0) = m*0 + c  = c

p(0) = 6

=> c = 6

hence

p(w) = mw + 6

for w = 7 , p = 83

=> p(7) = 7m + 6

p(7) = 83

=> 7m + 6 = 83

Subtracting 6 from both sides

=> 7m = 77

dividing by 7 both sides

=> m = 11

p(w) = 11w + 6

After n weeks => w = n

=> p(n) = 11n + 6