Question

A scientist studying insects starts with a population of 10. The population triples every hour. How many insects will there be after 20 minutes?

Answer 1

Not so fast.... maybe it triples every hour, but doesn't mean that anything during the 20 minutes happens.\[10(3)^{k}\] would be the sequence that says it in terms of hours.

But, will assume so, that it changes with the same ratio after 20 minutes as after an hour.
for the sake of the asker :)

10 .... would turn into 30 after the 1st hour



find some geometric means .

\[10~~~~~~~~~~~~~~~~~~~~~~~~~~\text{__},~~~~~~~~~~~~~~~~~~~~~~~~~~\text{__},~~~~~~~~~~~~~~~~~~~~30\]
at first after 20 min after 40 minutes after an hour.

Answer 2

After 20 minutes is the first geometric mean,
After 40 minutes is the second geometric mean.

To find the common ratio,
\[10 \times r^{3}=30\]\[r^{3}=3\]\[r=\sqrt[3]{3}≈1.44\]

Answer 3

\[10 \times \sqrt[3]{3}~~~~~or,~~~~approximately~~~~~~10 \times 1.44~~~~is~~\]\[what's~~~after~~~20~~~\min.\]