A weight lifter can bench-press 145 pounds. She plans to increase the weight \( W(x) \) in pounds that she is lifting according to the function \( W(x) = 145(1.05)^x \), where \( x \) represents the number of training cycles she completes. How much will she bench-press after 5 training cycles?

Question

High School

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Answer :

eramkhanvt eramkhanvt · Answer 1 · 2024-07-27T18:02:31-04:00

After 5 training cycles, the weight lifter will be able to bench-press is, 170.93 pounds.

We have,

The function is,

W(x) = 145(1.05)ˣ represents the weight she is lifting after completing x training cycles.

In this case, x is 5,

so we substitute the value into the function.

W(5) = 145 (1.05)ˣ

= 145(1.27628)

= 170.93 pounds.

The function W(x) = 145(1.05) is an exponential growth function, where the weight being lifted increases over time.

The base of the exponential function, 1.05, represents the rate of growth.

In this case, the rate of growth is,

1.05 - 1 = 0.05 or 5%

Each time the weight lifter completes a training cycle, the weight she is lifting is multiplied by 1.05.

Hence, After 5 training cycles, the weight lifter has multiplied the initial weight of 145 pounds by 1.05 five times,

= 145 x 1.05

= 170.93 pounds.

So, This demonstrates the compounding effect of exponential growth, where the weight being lifted gradually increases with each training cycle.

Therefore, after completing 5 training cycles, the weight lifter will be able to bench-press approximately 170.93 pounds.

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