David earns 4% for the money he has in savings. let a represent how much he has in his account. write two expressions that can be used to calculate the amount of money in his account after one month

I = a/300

A = (300I + a)/300

Step-by-step explanation:

David earns 4% for the money he has in savings. Let the amount that he has initially be a. This means that his principal is a. So

P = a

The rate at which he is earning interest on the principal is 4%. Therefore,

R = 4℅

We want to calculate the amount of money in his account after one month. This means that time,

t = 1/12 (12months make a year)

The amount of money in his account after one month will be the interest earned in one month + the initial amount in the account.

To determine the interest, we will apply the simple interest formula,

I = PRT/100

Where I = interest

P = principal

T = time

The first equation will be

I = (a × 4 × 1)/12 × 100

I = 4a/1200 = a/300

The second equation will be

Amount in the account after one month,A

A = I + a/300

A = (300I + a)/300

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

answer: answer is b.

[m < b = 120º]

step-by-step explanation: