a scientist records the number of cells in a culture. the function f(x) = 1,600(1.35)^x describes f, the number of cells in the culture after x hours. which statement best describes one value in this function

Question

a. the number of cells increases at a rate of 135% per hour.
b. the number of cells increases by 135 per hour.
c. the initial number of cells in the culture is 2,160.
d. the initial number of cells in the culture is 1,600

Answer 1

To analyze the function \( f(x) = 1,600(1.35)^x \):

1. Understanding the parameters: The constant \( 1,600 \) represents the initial number of cells when \( x = 0 \). Therefore, this value indicates how many cells are in the culture at the start.

2. Growth rate: The \( 1.35 \) base in the exponential function implies a growth factor. Specifically, this means that the number of cells increases by \( 35% \) each hour (not \( 135% \), which can be misleading).

Now, let's evaluate each statement:

a. The number of cells increases at a rate of 135% per hour.

• This is incorrect. The growth factor \( 1.35 \) means an increase of \( 35% \) per hour.

b. The number of cells increases by 135 per hour.

• This is also incorrect. The growth is exponential, not a fixed amount added per hour.

c. The initial number of cells in the culture is 2,160.

• This statement is false. The initial number, when \( x = 0 \), is \( 1,600(1.35)^0 = 1,600 \).

d. The initial number of cells in the culture is 1,600.

• This statement is true, as previously noted.

Thus, the statement that best describes one value in this function is:

d. The initial number of cells in the culture is 1,600.