Mark M. answered • 02/05/20

Mathematics Teacher - NCLB Highly Qualified

f(x) = a_{0}(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

Eva M.

asked • 02/05/20**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?**

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Mark M. answered • 02/05/20

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Mathematics Teacher - NCLB Highly Qualified

f(x) = a_{0}(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

Hi Eva

Here's how you think about it...

Let us call the newborn weight x. In this example, X_{0} = 0.06 gm.

After day 1, the weight will increase by 10%, i.e.by 0.1X_{0}

So, weight after day 1,

X_{1} = X_{0.}+0.1X_{0 }

_{ }= X_{0}.(1 +0.1) ------- (1)

Weight after day 2, X_{2} = X_{1}.(1+0.1)

Substitute for X1 from equation (1)

X_{2 }= X_{0}.(1 +0.1)^{2}

Similarly, you can calculate Weight after day 3,

X_{3 } = X_{2} + 0.1X_{2}

_{ }Or,_{ }X_{3 = } X_{0}.(1 +0.1)^{3}

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

Weight after day 'n'

Xn = X_{0}.(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 X_{0} = 0.06 gm, you can estimate the weight to be approx 3.28 gm

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