Question

a scientist records the number of calls 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?
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 cultural is 1,600

Answer 1

To analyze the function \( f(x) = 1,600(1.35)^x \), let's break down the statements:

1. **Initial Number of Cells**:
- When \( x = 0 \), we find the initial number of cells:
\[
f(0) = 1,600(1.35)^0 = 1,600 \times 1 = 1,600
\]
This makes statement **d** correct: "the initial number of cells in the culture is 1,600."

2. **Rate of Increase**:
- The function \( (1.35)^x \) indicates that the number of cells increases by a factor of 1.35 for each hour. This means the cells are increasing by 35%, not 135%. Thus, statement **a** is incorrect.

3. **Increase by a Constant Amount**:
- The function does not state an increase by a fixed amount per hour (such as 135), but instead increases by a percentage. Therefore, statement **b** is incorrect.

4. **Initial Number Misstatement**:
- Statement **c** suggests that the initial number of cells is 2,160, which is false based on our calculation.

Thus, the statement that best describes one value in this function is:
**d**: the initial number of cells in the culture is 1,600.