Problem 35 - Beginning and Intermediate Algebra

Question

Carlton wants to improve his bench press. He plans on adding 10 Ib to the bar each week. If he can lift 100 Ib this week, how much will he lift 6 weeks from now?

Step-by-Step Solution

Answer

Carlton will be able to lift \(160\) lb 6 weeks from now.

Step 1: Define the given values

Carlton starts by lifting 100 lb and plans to add 10 lb each week. We are to find the weight he'll lift 6 weeks later.

Step 2: Calculate the total weight added after 6 weeks

Since Carlton adds 10 lb each week, we need to find the total weight he adds after 6 weeks. To do that, we can multiply the weekly increase (10 lb) by the number of weeks (6). Total weight added = Weekly increase × Number of weeks Total weight added = 10 lb × 6 = 60 lb

Step 3: Calculate the weight Carlton will lift in 6 weeks

Now, we need to add the total weight added (60 lb) to his initial weight (100 lb) to find how much he will lift after 6 weeks. Weight after 6 weeks = Initial weight + Total weight added Weight after 6 weeks = 100 lb + 60 lb = 160 lb So, Carlton will be able to lift \(160\) lb 6 weeks from now.

Key Concepts

Linear Growth

Linear growth is a way to describe situations where there is a consistent increase or decrease over time. In the exercise, Carlton adds 10 lb to his bench press weight each week. This steady increase is a perfect example of linear growth.

To understand linear growth in arithmetic sequences, consider these key points:

• The amount of increase (10 lb) stays constant every time period (week).
• The starting point (100 lb in the first week) is essential for calculating future values.
• For each week, you add the constant amount to the previous total.

Linear growth contrasts with exponential growth, where the increase would become larger over time. Instead, in linear growth, the increase is always the same, making it straightforward to calculate future outcomes.

Weight Training

Weight training involves strength-building exercises where you lift weights in various forms. People often set goals, like increasing the weights they can lift over time, which fits well with concepts like linear growth.

For Carlton, his goal was to enhance his bench press capacity:

• He began with a base weight of 100 lb, which he could comfortably manage.
• He set an achievable increase target, 10 lb per week, to avoid overexertion.
• His gradual increase in weight lifts aligns with best practices, preventing injury while promoting steady muscle development.

When pursuing weight training, it's crucial to follow a balanced approach. Steady increments are preferred as they allow muscles to adapt, build, and reduce the risk of injury.

Mathematical Modeling

Mathematical modeling is a powerful tool that helps us understand and solve real-life problems by representing them in mathematical terms. In Carlton's weight-lifting exercise, we made use of mathematical concepts to predict future achievements based on current actions.

Here's how mathematical modeling worked in this scenario:

• We defined the problem by identifying the initial weight (100 lb) and the weekly increase (10 lb).
• We established an arithmetic formula to find the total increase over 6 weeks: 10 lb multiplied by 6 weeks equals 60 lb.
• Finally, we added this total increase to the initial weight, giving us Carlton’s new target of 160 lb in 6 weeks.

This model provides a realistic outlook, allowing Carlton to measure progress effectively. Mathematical modeling enables planning and assessing various scenarios by breaking down complex processes into manageable computations.