A goliath monster is about 16 cm long at birth during the beginning of its life. The glider monsters length increases by about 15% each week write a function that models the length of the glider monster at the beginning of the glider monsters life use ask for the number of weeks and why for the length of the Gila monster y=16( )^x

Answer 1

To create a function that models the growth of the glider monster, we'll start with the initial length and the growth rate.

The initial length of the goliath monster ( \( y_0 \) ) is 16 cm, and it grows by 15% each week. This means it retains 100% of its length while adding an additional 15%, which can be expressed as a growth factor of \( 1 + 0.15 = 1.15 \).

The function modeling the length of the goliath monster after \( x \) weeks can be expressed as:

\[ y = 16(1.15)^x \]

In this formula:

• \( y \) is the length of the goliath monster after \( x \) weeks.
• \( 16 \) is the initial length in cm.
• \( 1.15 \) is the growth factor, as the monster grows by 15% each week.
• \( x \) is the number of weeks.

So, if you want to find out how long the goliath monster will be after a certain number of weeks, you would substitute \( x \) with the number of weeks into the equation.

For example, if you want to know the length after 5 weeks:

\[ y = 16(1.15)^5 \]

You can calculate this to find the length at that time.

Answer 2

Find the length of the gila Monster at the end of the three weeks round your answer to the nearest 10th one decimal place

Answer 3

To find the length of the goliath monster at the end of 3 weeks using the growth model we established earlier:

\[ y = 16(1.15)^x \]

Substituting \( x = 3 \):

\[ y = 16(1.15)^3 \]

Now, let's calculate \( (1.15)^3 \):

\[ (1.15)^3 = 1.15 \times 1.15 \times 1.15 \approx 1.520875 \]

Now substitute this back into the equation:

\[ y = 16 \times 1.520875 \approx 24.334 \]

Rounding to the nearest tenth, we get:

\[ y \approx 24.3 \text{ cm} \]

So, the length of the goliath monster after 3 weeks is approximately 24.3 cm.