Question

A young channel catfish increases by about 23% each week. Write an exponential growth function that represents the weic y=0.1(1.23)ᵗAbout how much will the catfish weigh after 4 weeks?

Answer 1

The weight of the channel catfish after 4 weeks, based on the exponential growth function y = 0.1(1.23)t, would be approximately 0.229297 pounds. Calculating this involves plugging in 4 for the value of t and following the order of operations.

Step-by-step explanation:

The student is asking about calculating the future weight of a channel catfish using an exponential growth function. The formula provided is y = 0.1(1.23)t, where t is the time in weeks. To find the weight after 4 weeks, we would substitute t with 4, yielding y = 0.1(1.23)⁴.

Now, let's calculate the weight:

1. y = 0.1(1.23)⁴
2. y ≈ 0.1(2.29297)
3. y ≈ 0.229297

After 4 weeks, the channel catfish will weigh approximately 0.229297 pounds.

It's crucial to understand the nature of exponential growth, as it represents a situation where the rate of increase grows proportionally to the current size, leading to a rapid escalation over time. This concept is applicable to many real-world scenarios, from finance to biology.