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SVEN [57.7K]
2 years ago
12

The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Marco is stu

dying the change in the amount of money in two accounts, A and B, over time.
The amount f(x), in dollars, in account A after x years is represented by the function below:
f(x) = 1,264(1.08)^x

**need help on part A and part B–correct answers only please**

Mathematics
1 answer:
sasho [114]2 years ago
4 0

Answer:

Step-by-step explanation:

Account A: Decreasing at 8 % per year

Account B: Decreasing at 10.00 % per year

The amount f(x), in dollars, in account A after x years is represented by the function below:

f(x) = 10,125(1.83)x

Account B shows the greater percentage

change

Step-by-step explanation:

Part A: Percent change from exponential

formula

f(x) = 9628(0.92)*

The general formula for an exponential

function is

y = ab^x, where

b = the base of the exponential function.

if b < 1, we have an exponential decay

function.

f(x) decreases as x increases.

Account A is decreasing each year.

We can rewrite the formula for an

exponential decay function as:

y= a(1 – b)”, where

1- b = the decay factor

b = the percent change in decimal

form

If we compare the two formulas, we find

0.92 = 1- b

b = 1 - 0.92 = 0.08 = 8 %

The account is decreasing at an annual rate of 8%. The account is decreasing at an annual rate of 10.00%.

Account B recorded a greater percentage change in the amount of money over the previous year.

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The chairs in the auditorium illustrates an arithmetic sequence

  • The recursive rule is:  an = an-1 + 8; a1 = 26
  • The explicit rule is:  an = 18 + 8n
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<h3>The recursive rule</h3>

From the question, we have the following sequence:

Seats: 18, 26, 34

Rewrite as:

26 = 18 + 8

34 = 26 + 8

The above means that:

The number of seats on a row is 8 added to the the number of seats on the previous row.

Hence, the recursive rule is:

an = an-1 + 8; a1 = 26

<h3>The explicit rule</h3>

In (a), we have:

a1 = 26 and d = 8

The explicit rule is calculated using:

an = a1 + (n -1) * d

This gives

an = 26 + (n - 1) * 8

Expand

an = 26 - 8 + 8n

Evaluate the difference

an = 18 + 8n

Hence, the explicit rule is:

an = 18 + 8n

<h3>The number of seats in the row 7</h3>

This means that n = 7.

So, we  have:

a7 = 18 + 8 * 7 = 74

Hence, there are 74 seats in the 7th row

<h3>The sigma notation</h3>

We have the maximum number of rows to be 12.

So, the sigma notation would be:

\sum\limits^{12}_{n=1} {18 + 8n}

The total number of seats is:

Sn = n/2(2a + (n -1) * d)

This gives

S12 = 12/2(2 * 26 + (12 -1) * 8)

S12 = 840

Hence, 840 chairs can fit the auditorium

Read more about arithmetic sequence at:

brainly.com/question/6561461

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