Question

A young channel catfish weighs about 0.5 pounds during the next 8 weeks its weight increases by about 24.5% each week. predict what the weight would be after 7 weeks round two decimals?

Answer 1

2.32 pounds

Step-by-step explanation:

Given:

U₁ = 0.5 pounds

r = 100% + 24.5% = 1.245

n = 7 + 1 = 8

`\boxed{U_n=U_1\cdot r^((n-1))}`

`U_n=0.5*1.245^((8-1))`

`=2.32\ pounds`

Answer 2

To predict the weight of the catfish after 7 weeks with a weekly growth rate of 24.5%, we use the exponential growth formula and calculate it to be approximately 1.37 pounds when rounded to two decimals.

Step-by-step explanation:

To predict the weight of a channel catfish after 7 weeks, given that it initially weighs 0.5 pounds and increases by about 24.5% each week, we can use the formula for exponential growth: final weight = initial weight × (1 + growth rate)number of weeks. The growth rate in this case is 24.5%, which as a decimal is 0.245.

Now let's calculate:

1. Convert the percentage increase to a decimal by dividing 24.5 by 100: 0.245.
2. Calculate the growth factor by adding 1 to the decimal growth rate: 1 + 0.245 = 1.245.
3. Apply the growth factor to the initial weight for 7 weeks: (0.5) × (1.245)7.
4. Perform the exponentiation and multiplication to find the final weight.

So, the final calculation will look like this:

Final weight = 0.5 × (1.245)7 = 0.5 × 2.7379 ≈ 1.37 pounds.

Therefore, the predicted weight of the catfish after 7 weeks would be approximately 1.37 pounds when rounded to two decimals.