The initial population of an ant colony was approximately $600$. The population grows at a rate of $12\%$ per week.

Find the approximate number of ants in the colony after $15$ weeks and after $30$ weeks. (Round off to nearest integer)

The initial population of an ant colony was approximately $600$. The population grows at a rate of $12\%$ per week.

Graph the function. Use the graph to estimate how many weeks the ant population takes to double in size.

A population of $10000$ insects decreases by $9\%$ every year.

Write down a formula and use it to calculate the number of insects left after $3$ years.

A population of $10000$ insects decreases by $9\%$ every year.

Write down a formula and use it to calculate the number of insects left after $10$ years.

A population of $10000$ insects decreases by $9\%$ every year. If the time taken for the insect population to reduce to less than half its percent size is $k$ years, then find the value of $k$ (rounded off and write up to $2$ decimal places).

Sahil's parents invest $\$5000$ in a long-term money fund offering $4\%$ interest compounded annually. If it will takes $x$ years for this amount to double, then find the value of $x$ (correct upto the nearest whole number).

Conservationists estimate that there are $80$ wolves in a forest and that the population is decreasing at a rate of $3.5\%$ per year. If the time taken for the present population to be halved is $x$ years, then find the value of $x$ (rounded off to one decimal place). Take $\log 0.5=-0.3010$ and $\log 0.965=-0.0154$.

An antibiotic destroys $10\%$ of bacteria present in one hour. If it takes $x$ hours for the antibiotic to reduce $50$ million bacteria down to less than $1$ million bacteria, find the value of $x$. (Round off the answer to nearest integer) [Use $\log 0.02=-1.6989$ and $\log 0.9=-0.0457$]

You are given the function $f\left(x\right)=3^x$.

a. Describe each transformation of $f(x+2)$ in words.

b. Write the transformed function as $g\left(x\right)=$_____

c. Sketch both the function and transformed function on the same set of axes.