Question

Please make sure you answer both parts of the question. Remember to properly format your function.The hat that George bought turned out to previously belong to a magician! Initially, 3 rabbits hopped out of the hat. Each day after that, double thenumber of rabbits from the previous day appeared.1: Write an exponential function that can be used to model this function.2: How many rabbits appeared on the 13th day?

Answer 1

Question 1:

`\begin{gathered} \text{ On day 1, 3 rabbits hopped out} \\ \text{ On day 2, }3*2=6\text{ rabbits hopped out} \\ \text{ On day 3, }3*2*2=3*2^2\text{ rabbits hopped out} \\ \text{ On day 4, }3*2*2*2=3*2^3\text{ rabbits hopped out} \\ \\ \text{Following this pattern, we can find the number of rabbits that will hop out on a day n.} \\ \\ \text{ On day }n,3*2*2*2\ldots*2=3*2^(n-1)\text{ rabbits hopped out} \\ \\ \text{Thus, the exponential function to model this scenario is given below as } \\ \\ f(n)=3*2^(n-1) \end{gathered}`

Question 2:

`\begin{gathered} \text{The question is asking for the number of rabbits that will hop out on day 13} \\ \text{ We can simply apply our formula and this implies that }n=13 \\ \\ \therefore f(13)=3*2^(13-1) \\ \\ f(13)=3*2^(12)=12,288 \\ \\ \text{Thus, the number of rabbits that will hop out of the hat on the 13th Day is 12,288} \end{gathered}`

Final Answer

Question 1:

The exponential function to model the scenario is

`f(n)=3*2^(n-1)`

Question 2:

The number of rabbits that will hop out of the hat on the 13th Day is 12,288 rabbits