Question

A and b are natural numbers. the diameter of cell a is 2.3 , and 10 rasied to power the diameter of cell b is 2.3 raised to a power . Which is a true statement?

A) \( A = 2.3 \)
B) \( B = 2.3^{\text{a power}} \)
C) \( A = 10 \)
D) \( B = 10^{\text{a power}} \)

Answer 1

Statement D) B = 10^a power is the true statement. This is because it reflects the given that 10 raised to the diameter of cell B fits the format of a base 10 number raised to a power, representing 'B'.

Step-by-step explanation:

The question involves understanding exponential relationships and powers of numbers. Given that 'A' and 'B' are natural numbers, with the diameter of cell 'A' being 2.3, and the statement that 10 raised to the power of the diameter of cell 'B' is the same as 2.3 raised to a power, we are looking for a true statement about these relationships.

Since 'A' is the diameter of cell A, and we have no information that 'A' equals 2.3, statement A) A = 2.3 is not necessarily true. Regarding statement B) B = 2.3a power, we only know that 10 is raised to the power of the diameter of cell B, so we cannot conclude that 'B' is equal to 2.3 raised to any power without additional information. Statement C) A = 10 cannot be true as 'A' is explicitly stated to be 2.3. However, statement D) B = 10a power is true because it matches the description of cell B: 10 raised to the diameter of cell B is the same format as 10 to an exponential power, which in turn is a power of 'B'.