The function f(x) = 7(1.32)^x models the number, in billions, of the DNA sequences in a database x years since 2010. What does the 1.32 represent?

Question

Responses
A The annual increase rate in sequences is 32%.The annual increase rate in sequences is 32%.
B The total increase rate in sequences since 2010 is 32%.The total increase rate in sequences since 2010 is 32%.
C The increase rate in sequences before 2010 was 32%.The increase rate in sequences before 2010 was 32%.
D The starting number of sequences in 2010 was 1.32 billion.

Answer 1

The function \( f(x) = 7(1.32)^x \) represents exponential growth where the base \( 1.32 \) indicates the growth factor for each year. In this context, the base \( 1.32 \) can be interpreted as an annual increase rate.

To understand what \( 1.32 \) represents, we can break it down:

• If the growth factor is \( 1.32 \), this means that each year the quantity (number of DNA sequences, in billions) increases to 132% of its value in the previous year.
• This indicates a 32% increase from the previous year because \( 1.32 - 1 = 0.32 \) or 32%.

Therefore, the correct answer is:

A: The annual increase rate in sequences is 32%.