Question

Suppose a colony of mushrooms triples in size every 10 days. If there are 10 mushrooms to start, how many days until there are 1000 mushrooms? (A) 41.9181 days (B) 56.4091 days (C) 37.9010 days (D) 29.8974 days (E) 49.3955 days

Answer 1

Approach1: Genral Approach

Given, mushrooms triples in size every 10 days

it started with 10 mushrooms to begin.

for first 10 days, it becomes triple i.e 30.

similarly, we can represent it in tabular form:

No.of days	No.of mushrooms
10	30
20	90
30	270
40 days	270X3 =810 mushrooms

After this, in next 10 days, the count will cross 1000. i.e in next 10 days, total count will incresse by 1620 along with already present 810 mushrooms. So, for every single day, count increases by 162.

So, after 41 days, count will become 810+162 = 972 and after 41.9181 days count will become 1000.

Approach2: Power function approach

For every 10 days, the count becomes triple.

after how many multiple of 10 (n) days, the count becomes 1000.

given by the function:

So, 1000= 3ⁿ X 10

3ⁿ=100

apply logarithm on both sides, we get

n = log 100/ log3

n = 4.1918065485787692085931350440428

So, in 10n days, the count becomes 1000.

implies, 41.9181 days is the answer.