Pls help me out, I really need help.

A puppy weighs 0.85 lb at birth, and each week he gains 29% in weight. Let an be his weight in pounds at the end of his nth week of life.
(a) Find a formula for an.
an =


(b) How much does the puppy weigh when he is six weeks old? (Round your answer to one decimal place.)
a6 =
lb

an = 0.85 * 1.29^n

Now just plug in n=6

(a) To find a formula for an, we can start by looking at the pattern of weight gain.

At the end of each week, the puppy gains 29% of its current weight. This can be expressed as multiplying the current weight by 1.29 (100% + 29% = 129%).

Therefore, we can write the formula for an as follows:
an = an-1 * 1.29

This formula indicates that the weight at the end of week n is the weight at the end of week n-1 multiplied by 1.29.

(b) To find how much the puppy weighs when he is six weeks old (a6), we can use the formula an = an-1 * 1.29 repeatedly.

Starting with the weight at birth (a0), we can calculate the weight at 6 weeks using the formula:

a1 = a0 * 1.29
a2 = a1 * 1.29
a3 = a2 * 1.29
a4 = a3 * 1.29
a5 = a4 * 1.29
a6 = a5 * 1.29

Since we know that a0 = 0.85 lb, we can substitute this value into the formula:

a1 = 0.85 * 1.29
a2 = (0.85 * 1.29) * 1.29
a3 = [(0.85 * 1.29) * 1.29] * 1.29
a4 = [[(0.85 * 1.29) * 1.29] * 1.29] * 1.29
a5 = [[[ (0.85 * 1.29) * 1.29] * 1.29] * 1.29] * 1.29
a6 = [[[[ (0.85 * 1.29) * 1.29] * 1.29] * 1.29] * 1.29] * 1.29

Evaluating this expression will give us the weight at 6 weeks, rounded to one decimal place.

Sure! I can help you with that.

To find a formula for an, the weight of the puppy at the end of the nth week, we'll need to use the information provided. We know that the puppy weighs 0.85 lb at birth, so we'll start with that.

Each week, the puppy gains 29% in weight. To calculate the weight for each week, we can multiply the previous week's weight by 1.29. Let's use a recursive formula to represent this:

a1 = 0.85 (weight at birth)
an = 1.29 * an-1 (weight after n weeks, where n > 1)

Now, let's find the weight of the puppy when he is six weeks old. We can use the formula we just derived and substitute n = 6:

a6 = 1.29 * a5
= 1.29 * (1.29 * a4)
= 1.29 * (1.29 * (1.29 * a3))
= 1.29 * (1.29 * (1.29 * (1.29 * (1.29 * a1))))
= 1.29^5 * a1 (since a1 = 0.85)

We can now calculate the value of a6 using the formula we derived. Let's do the calculations:

a6 = 1.29^5 * a1
= 1.29^5 * 0.85
≈ 2.253 * 0.85
≈ 1.91525

Therefore, when the puppy is six weeks old, he weighs approximately 1.9 pounds, rounded to one decimal place.

I hope this explanation helps! Let me know if you have any further questions.