Can someone give me a growth and decay word problem solve it and explain how you arrive at the final answer in a way I understand it.
Thanks ahead of time.
you saying that your text has no such problems worked out? How will reading such a problem here make it any easier?
Thanks anyway I have been at this for 6 hours I found someone to help me understand.
I appreciate your kindness.
Of course! I can provide you with a growth and decay word problem and walk you through the process of solving it step by step.
Let's consider the following word problem:
"The population of a city is currently 200,000 people. It is projected to decrease by 5% each year. How many people will be in the city after 4 years?"
To solve this problem, we will use the formula for exponential decay:
Final amount (A) = Initial amount (P) × (1 - rate)^time
Step 1: Identify the given information:
- Initial population (P) = 200,000 people
- Decay rate (rate) = 5% = 0.05
- Time (years) = 4 years
Step 2: Plug in the values into the formula:
A = 200,000 × (1 - 0.05)^4
Step 3: Solve the equation:
A = 200,000 × (0.95)^4
Step 4: Simplify the equation using exponents:
A = 200,000 × 0.8145
Step 5: Calculate the final amount (A):
A ≈ 162,900
Therefore, after 4 years, the city is projected to have approximately 162,900 people.
By following these steps, we used the formula for exponential decay, identified the given information, plugged the values into the formula, simplified the equation, and obtained the final result.