Question

Write an equation to model growth or decay in the following scenario. A stock is declining at a rate of 25% of its value every 2 weeks. The stock started at $225. Let a represent the number of weeks. Let y represent the value of the stock in dollars.
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Answer 1

The exponential function that models this situation is:

$y(t) = 225(0.75)^{\frac{t}{2}}$

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A decaying exponential function has the following format:

$y(t) = y(0)(1 - r)^t$

In which:

• y(0) is the initial value.
• r is the decay rate, as a decimal.

In this problem:

• The stock started at $225, thus $y(0) = 225$.
• Declines at a rate of 25% every 2 weeks, thus $r = 0.25, t = \frac{t}{2}$

The equation is:

$y(t) = y(0)(1 - r)^t$

$y(t) = 225(1 - 0.25)^{\frac{t}{2}}$

$y(t) = 225(0.75)^{\frac{t}{2}}$

A similar problem is given at brainly.com/question/24282972