Function Word Problem: If you invest $x at 4%, then....

[FalconPUNCH!]

I'm horrible at word problems. I can do the math correct but I don't know how to set up these problems. Can someone help me with it. I can do the math and everything myself but I don't know where to approach this problem. This is for my Calc 1 class. I don't understand the n part.

If you invest x dollars at 4% interest compounded annually, then the amount A(x) of the investment after one year is A(x) = 1.04x. Find AoA, AoAoA, and AoAoAoA. What do these compositions represent? Find a formula for the composition of n copies of A.

 

[tkhunny]

Re: Function Word Problem

I'm horrible at word problems. I can do the math correct but I don't know how to set up these problems. Can someone help me with it. I can do the math and everything myself but I don't know where to approach this problem. This is for my Calc 1 class.

If you invest x dollars at 4% interest compounded annually, then the amount A(x) of the investment after one year is A(x) = 1.04x. Find AoA, AoAoA, and AoAoAoA. What do these compositions represent? Find a formula for the composition of n copies of A.

1) Give yourself a break, play less Smash Brothers, and pay attention in class.

2) This is the same as any other composition.

\(\displaystyle AoA = A(A(x)) = 1.04(A(x)) = 1.04(1.04x) = 1.04^{2}(x)\)

 

[FalconPUNCH!]

Re: Function Word Problem

I'm horrible at word problems. I can do the math correct but I don't know how to set up these problems. Can someone help me with it. I can do the math and everything myself but I don't know where to approach this problem. This is for my Calc 1 class.

If you invest x dollars at 4% interest compounded annually, then the amount A(x) of the investment after one year is A(x) = 1.04x. Find AoA, AoAoA, and AoAoAoA. What do these compositions represent? Find a formula for the composition of n copies of A.

1) Give yourself a break, play less Smash Brothers, and pay attention in class.

2) This is the same as any other composition.

\(\displaystyle AoA = A(A(x)) = 1.04(A(x)) = 1.04(1.04x) = 1.04^{2}(x)\)

I don't play games as much as I used to. School is a higher priority. I understand the first part. I don't really understand the N part.

Edit: Thank you for your help

 

[FalconPUNCH!]

The answer I came up for the n part is A(x) = 1.04^(n+1)(x)

 

[Deleted member 4993]

The answer I came up for the n part is A(x) = 1.04^(n+1)(x) .... Incorrect

Composition of 2 copies A = A o A = x(1.04)^2

Composition of 3 copies A = A o A o A = x(1.04)^3

Composition of 4 copies A = A o A o A o A = x(1.04)^4

Composition of n copies A = A o A ....o A o A = x(1.04)^n

 

[FalconPUNCH!]

[quote="FalconPUNCH!":19ll6ag4]The answer I came up for the n part is A(x) = 1.04^(n+1)(x) .... Incorrect

Composition of 2 copies A = A o A = x(1.04)^2

Composition of 3 copies A = A o A o A = x(1.04)^3

Composition of 4 copies A = A o A o A o A = x(1.04)^4

Composition of n copies A = A o A ....o A o A = x(1.04)^n[/quote:19ll6ag4]Thanks...I got the N one earlier. I realized what I did wrong. Thank you anyways.