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