Rewrite the function $f\left(x\right)=9^x$ with a base of $81$. Then describe how you can graph this function using $81$ as a base, in the form $y={81}^{ax}$.

One bacterium cell divided to produce two cells every minute.

Write down a function for the number of cells after $x$ minutes.

One bacterium cell divided to produce two cells every minute. Calculate the number of cells after $15$ minutes.

One bacterium cell divided to produce two cells every minute.

If the number of cells after half an hour is $k$, then value of $k$ is ......

One bacterium cell divides to produce two cells every minute. Graph the function to determine when there will be $1$ million cells (after how many minutes). (Round off and write your answer to the nearest integer) [Use $\log 2=0.301$]

The half-life of carbon-$11$ is $20$ minutes.

A  sample of carbon-$11$ has $10000$ nuclei. Make a table of values for five $20$-minute intervals and write a function for the number of nuclei after $x$ number of $20$ minute intervals.

The half-life of carbon-$11$ is $20$ minutes. A sample of carbon-$11$ has $10000$ nuclei. Find the number of nuclei after $3$ hours. (Round the answer to the nearest integer)

The half-life of carbon-$11$ is $20$ minutes. A sample of carbon-$11$ has $10000$ nuclei. If it takes $x$ minutes for the number of nuclei to reduce less than $10\%$ of the original number, then find the value of $x$ (correct up to one decimal place). [Use $\log 0.5=-0.301$]

Drug testing trials show that the amount of a pain-relieving medicine in a person's body reduces by one quarter every hour. It is safe to take another dose of the medicine when there is less than $200 \mathrm{mg}$ in the body. If it is safe to take another dose after $x$ hours of a dose of $400 \mathrm{mg}$, then find the value of $x$ (rounded off to one place of decimal).