Which of the following sentences is a declarative sentence? what will they think of next? we live in an amazing time. i simply adore cheese! tidy your room.

There are four types of sentences.  I'll list them below.

Interrogative sentences are questions: statements that end in a question mark (?).  "What will they think of next?" is an interrogative sentence, as you can see from the question mark, so we can rule this one out.

Exclamatory sentences are statements that end in an exclamation point (!).  "I simply adore cheese!" is one, because of its exclamation point, so this one isn't declarative either.

Now, things get a little trickier.  There are two types of sentences that end in a period (.): imperative and declarative sentences.

Imperative sentences are commands--telling someone to do something.  Which is imperative?  "Please tidy your room."  "We live in an amazing time."  Obviously, "Please tidy your room" is an order, and so is imperative.

The only sentence left is "We live in an amazing time."  This has to be a declarative sentence, which is simply a statement that ends in a period.  This is a statement, and it ends in a period, so this sentence is a declarative sentence.

We live in an amazing time.