The function H gives the height, above the ground, of a point on a spinning wheel. The function A gives the height of a point on a different spinning wheel and is defined by A(t)=1.2H(3t). Here, t, is time in seconds since the wheels started moving. How does the spinning wheel modeled by function A compare to the wheel for H? Explain how you know.

Barney is a dinosaur from our imagination

And when he's tall

He's what we call a dinosaur sensation

Barney's friends are big and small

They come from lots of places

After school they meet to play

And sing with happy faces

Barney shows us lots of things

Like how to play pretend

ABC's, and 123's

And how to be a friend

Barney comes to play with us

Whenever we may need him

Barney can be your friend too

If you just make-believe him!

Step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt