Question

There are bacteria in a petri dish. After 20 minutes, every bacterium splits into two. Explain how you can use the properties of exponents to write an expression for the resulting number of bacteria.

Answer 1

`T_n = (2^na)/(2)`

Explanation:

Given

Bacteria splits to 2 at every 20 minutes

Required

Explain how to get the resulting number of bacteria

To do this we simply make use of geometric progression formula;

`T_n = ar^(n-1)`

In this case; r = 2 (rate at which they split);

`T_n = a * 2^(n-1)`

a represents the initial number of bacteria in the dish

Apply law of indices

`T_n = a * (2^n)/(2^1)`

`T_n = a * (2^n)/(2)`

`T_n = (2^na)/(2)`

Assume, we want to determine the number of bacteria at the 10th 20 minutes (in other words, 200 minutes), the value of n will be 10