The number of psychiatry papers published each year decreases by 7%. if 26,000 papers were published in the current year, how many papers would be expected to be published in 5 years?.(round to nearest whole number)

Question

find a in this equation using y=a(b)^x
find base
find exponential equation
find how many papers are published after 5 years

Answer 1

To solve the problem, we'll use the formula for exponential decay, which is given by the equation:

\[ y = a(b)^x \]

where:

• \( y \) is the amount after \( x \) years,
• \( a \) is the initial amount,
• \( b \) is the base,
• \( x \) is the number of years.

Step 1: Identify \( a \) and \( b \)

1. Initial amount \( a \): This is the number of papers published in the current year, which is given as 26,000. Therefore, \( a = 26,000 \).

2. Base \( b \): Since the number of papers published decreases by 7% each year, we can express that as:

   \[ b = 1 - 0.07 = 0.93 \]

Step 2: Write the exponential equation

We can now construct the exponential equation:

\[ y = 26000(0.93)^x \]

Step 3: Calculate the number of papers published after 5 years

Now, we need to find out how many papers will be published after \( x = 5 \) years. We substitute \( x = 5 \) into the equation:

\[ y = 26000(0.93)^5 \]

Calculating \( (0.93)^5 \):

\[ (0.93)^5 \approx 0.6593 \]

Now substituting this back into the equation:

\[ y \approx 26000 \times 0.6593 \approx 17140.78 \]

Step 4: Round to the nearest whole number

Finally, rounding to the nearest whole number:

\[ y \approx 17141 \]

Summary

• Initial amount (\( a \)): 26,000
• Base (\( b \)): 0.93
• Exponential equation: \( y = 26000(0.93)^x \)
• Number of papers published after 5 years: 17,141.