How do I solve this??

Question

A newly hatched channel catfish typically weighs about 0.06 gram. During the first 6

weeks of life, its weight increases by about 10% each day. Write a function to model the

situation. How much does the catfish weigh after 6 weeks?

Answer 1

f(x) = a₀(r)^x Basic formula for growth/decay.

f(x) = 0.06(1.1)^x

f(42) = 0.06(1.1)⁴²

f(42) = 0.06(54.76)

f(42) = 3.2858

Answer 2

Hi Eva

Here's how you think about it...

Let us call the newborn weight x. In this example, X₀ = 0.06 gm.

After day 1, the weight will increase by 10%, i.e.by 0.1X₀

So, weight after day 1,

X₁ = X_0.+0.1X₀

= X₀.(1 +0.1) ------- (1)

Weight after day 2, X₂ = X₁.(1+0.1)

Substitute for X1 from equation (1)

X₂ = X₀.(1 +0.1)²

Similarly, you can calculate Weight after day 3,

X₃ = X₂ + 0.1X₂

Or, X_{3 =} X₀.(1 +0.1)³

Now you can see the pattern developing.. You can generalize this to

Weight after day 'n'

Xn = X₀.(1 +0.1)ⁿ

In a six week period there are 42 days. So you are asked to calculate the weight after 42 days. Using your calculator, and knowing X₀ = 0.06 gm, you can estimate the weight to be approx 3.28 gm