Question

The Lerna’s Hydra was a One-headed monster but when it is cut off, two more heads grow in its place. If a superhero tried to conquer it by cutting off its entire heads every day, (a) How many heads would the Hydra have on the fourth day? (b) And at the end of 15 days of trying to kill it, find the number of heads would Hydra have? Also, Express your answer in exponential form. (Hint: The first day, upon cutting the head off, the monster had two heads.)​

Answer 1

Answer:

Step-by-step explanation:

Assuming Hydra's head grows out next day only.

We start with 1 head, it turns 2 next day and keeps on doubling every day.

It will be a geometric progression with common ration (r) = 2 and initial term (a) = 1.

we know,

 n-term = ar^(n-1)

So, on 10th day

Number of head = 2^9  = 512