Question

Oliver planted four strawberry plants in his home garden. By the end of the first summer, all four plants each produced and developed two more plants. The second summer, the original four plants each produced and development two more plants again. Assuming the pattern continues, at the end of the fifth summer, how many strawberry plants will Oliver have in his garden given that there are an plants at the end of every n summers?

Answer 1

Let's define summer 1 as the year when Oliver planted the 4 plants.

At the end of summer 1 each plant produced 2 more plants, then now he has:

4*2 = 8 plants.

At the end of summer 2, this happens again:

Now he has

4*2*2 = 4*2^2 = 16 plants,

Then we can model the number of plants as a function of the number of summers.

P(s) = 4*2^(s)

s represents the number of summers that had been pass since the summer when he planted the initial 4 plants

When s = 0, we are in the first summer.

P(0) = 4*2^(0) = 4

So it is consistent.

Now we want to know the number of plants at the end of the fifth summer, this is:

P(5) = 4*2^5 = 128 plants.

And for the second question:

"how many strawberry plants will Oliver have in his garden given that there are an plants at the end of every n summers?"

Just replace s by n in the equation i wrote above:

P(n) = 4*2^n