Directions:Write an equation to model this scenario. Then use the equation to solve the problem.

Question

The number of dandelions growing on your lawn triples every 3 days. If your lawn started out with 15 dandelions how many would you have after 3 weeks?

Answer 1

a₀ = 15 

a₃ = 15 x 3 = 45

a₆ =45 x 3 = 135

a₉ = 135 x 3 = 405

 

Therefore you can see that every 3 days, you are multiplying by another 3.

 

So, the formula you can use is:

 

a_n = 15 x 3^(n/3)

 

So, for n = 21 days...

 

a₂₁ = 15 x 3^(21/3) = 15 x 3⁷ = 15 x 2187 = 32,805

So you would have 32,805 dandelions

 

Answer 2

t = number of days

 

n(t) = number of dandelions as a function of number of days

 

n₀ = initial population = 15

 

tripling period in days = 3

 

n(t) = n₀ (3)^t/3

 

t = (3 weeks)(7 days/week) = 21 days

 

n(21) = 15 (3)^21/3 = 15 (3)⁷ = ?