Let A(t) = 3- 2t^2 + 4^t. Find A(2) - A(1).

Answer 1

A(2) means that everywhere you see a 't', you put a '2' instead.

A(1) means that everywhere you see a 't', you put a '1' instead.

Once you solve those, you subtract.

A(2) = 3 - 2*(2²) + 4²

A(2) = 3 - 2*4 + 16

A(2) = 3 - 8 + 16

A(2) = 11

A(1) = 3 - 2*(1²) + 4¹

A(1) = 3 - 2*1 + 4

A(1) = 3 - 2 + 4

A(1) = 5

A(2) - A(1) = ?

11 - 5 = 6

Let me know if you have any more questions!

Answer 2

The function A is an instruction to do something with whatever gets put in it.

Specifically, if you put 't' into A, it will give back 3-2t^2+4^t.

So if you put 2 into A (called A(2)), you will get 3-2(2)^2+4^2 = 3-8+16=11.

Similarly, A(1) = 3-2(1)^2+4^1 = 3-2+4 = 5.

So A(2)-A(1) = 11-5 = 6.