Question

8.
write an equation to model the situation: in the body, a disease can multiply exponentially. each day what starts as just 5 cells will quadruple.

Explanation:

Step1: Identify the exponential growth formula

The general form of an exponential growth equation is $y = a \cdot b^x$, where $a$ is the initial amount, $b$ is the growth factor, and $x$ is the time variable.

Step2: Determine the values of \(a\) and \(b\)

• The initial number of cells (\(a\)) is 5, as given.
• The growth factor (\(b\)): Since the cells quadruple each day, \(b = 4\).
• Let \(x\) represent the number of days, and \(y\) represent the number of cells after \(x\) days.

Step3: Write the equation

Substitute \(a = 5\) and \(b = 4\) into the exponential growth formula: \(y = 5 \cdot 4^x\)

Answer:

\(y = 5 \cdot 4^x\) (where \(x\) is the number of days and \(y\) is the number of disease cells)