IBMediumSequences7–9

When Does the Culture Pass One Hundred Thousand

Quando é que a Cultura Passa os Cem Mil

A bacterial culture starts with $200$ cells and the number is multiplied by $3$ every hour. Write a formula for the number of cells after $n$ hours, find the number after $5$ hours, and find the first whole hour at which the culture passes $100000$ cells.

A fixed multiplier each hour is a geometric growth, so the hour number belongs in the exponent, not in a product. Watch where the count starts: at zero hours the culture is not yet multiplied.

Solution

Step 1 of 9

1.After $n$ hours: