Question

A and b are natural numbers. The diameter of cell a is 2.3 , and the diameter of cell b is 2.3 .

Which is a true statement?
A. If a = 4 and b = 6, then cell a is 100 times greater than cell b.
B. If a = 4 and b = 6, then cell b is 100 times greater than cell a.
C. If a = 4 and b = 6, then cell a is 2 times greater than cell b.
D. If a = 4 and b = 6, then cell b is 2 times greater than cell a.

Answer 1

After clarification we see the respective diameters are

`A = 2.3 * 10^(-a)`

`B = 2.3 * 10^(-b)`

We're asked about the ratio

`A:B = 2.3 * 10^(-a) : 2.3 * 10^(-b) = 10^(-a) : 10^(-b) = 10^b : 10^a = 10^(b-a) : 1`

Now we can go through the choices.

A. If a = 4 and b = 6, then cell a is 100 times greater than cell b.

`A:B=10^(6-4):1 = 100:1`

It would be more proper to say the diameter of cell A is 100 times the diameter of cell B, but yes, this is TRUE.

B. If a = 4 and b = 6, then cell b is 100 times greater than cell a.

FALSE. 10 to the minus 4 is 100 times bigger than 10 to the minus 6, so a is bigger.

C. If a = 4 and b = 6, then cell a is 2 times greater than cell b.

FALSE. We already calculated its 100 times bigger.

D. If a = 4 and b = 6, then cell b is 2 times greater than cell a.

FALSE.

Answer 2

A. If a = 4 and b = 6, then cell a is 100 times greater than cell b.

Explanation:

2.3/2.3= 1

10(-4)/10(-6)=10(2)

your answer is 100, cell a is 100 times greater than cell b.