50 super easy, 7th !

belinda wants to invest $1000. the table below shows the value of her investment under two different options for three different years:

number of years: 1 2 3

investment price: (amount in dollars) 1100 1210 1331

part a: write a function to describe the value of the investment f(n), in dollars, after n years.

part b: belinda wants to invest for 20 years. show the price of the investment after 20 years.

Part A:

Part B: f(20) ≈ $6727.5

Step-by-step explanation:

In this question you need to first observe the increment.

There you will notice that the increment is 10% of the previous element. For example:

In the first year, the increment is of $100 which is nothing but 10% of $1000. Therefore, the total sum of money is $100 + $1000 = $1100.

In the second year the increment is of $110 which is 10% of $1100. Now the total sum of money is $110 + $1100 = $1210

And So On...

Now, to make a function we need to observe some relation between the input value and the value of function at that input. This can be done by using the values of function given at some inputs.

We have f(0) = 1000

we also have f(1) = 1100 , f(2) = 1210 and f(3) = 1331

So, f(1) can be written as which is equal to 1100.

And, f(2) can be written as which equals to 1210.

We can write f(2) in terms of amount initially invested,i.e.,1000 as

similarly,

Therefore on observing the terms and the corresponding number of year

By using the above relation

Part B:

We have the following expression:
 sqrt 8 / x ^ 6
 Rewriting we have:
 sqrt (8 / x ^ 6)
 sqrt (2 * 4 / ((x ^ 2) * (x ^ 2) * (x ^ 2)))
 (2 / (x * x * x)) sqrt (2)
 (2 / x ^ 3) * sqrt (2)
 
 An equivalent expression is given by:
 (2 / x ^ 3) * sqrt (2)