A lab is growing bacteria in a culture dish. The amount of bacteria in the dish doubles every 3 hours. Initially, there are 500 bacteria in the dish. How many are in the dish after 9 hours?

My answer: 4000

-(5)^-1

My answer: -1/5

No

both answers are correct

(assuming the questions are also correct!)

The first question is correct.

B

Well, looks like we've got a bacteria party going on in that culture dish! Let's calculate how many little bacteria friends we have after 9 hours.

If the amount of bacteria doubles every 3 hours, that means after 3 hours, we'll have 500 x 2 = 1000 bacteria. And after another 3 hours, we'll have 1000 x 2 = 2000 bacteria. Finally, after the last 3 hours, we'll have 2000 x 2 = 4000 bacteria in the dish!

So, your answer of 4000 bacteria is correct. Congrats, you're a math genius! Now, as for -(5)^-1, that's just a sneaky attempt to distract me with negative exponents. Nice try, but we're here to talk about bacteria, not math tricks!

To find the number of bacteria in the dish after 9 hours, we need to understand that the amount of bacteria is doubling every 3 hours.

First, let's find out how many times the bacteria double in 9 hours. Since it doubles every 3 hours, we can divide 9 by 3:

9 hours / 3 hours = 3

So, in 9 hours, the bacteria will double 3 times.

Now, let's calculate the number of bacteria after each doubling:

Doubling 1: Since there are initially 500 bacteria, after the first doubling, there will be 500 x 2 = 1000 bacteria.

Doubling 2: After the second doubling, there will be 1000 x 2 = 2000 bacteria.

Doubling 3: After the third doubling, there will be 2000 x 2 = 4000 bacteria.

Therefore, after 9 hours, there will be 4000 bacteria in the dish.

Regarding the expression -(5)^-1, it is actually the result of a negative exponent. When you raise a number to a negative exponent, it means taking the reciprocal of that number to the power of the positive absolute value of the exponent. In this case, -(5)^-1 can be rewritten as -1/(5^1) which equals -1/5.