Question

NO LINKS!!!! URGENT HELP PLEASE!!!!

Please help me with #1 and #2

Answer 1

1a. Decay

1b. r = 0.43

1c. a = 35

1d. y = 6.481755

2a. Growth

2b. r = 2.23

2c. a = 225

2d. y = 340.4025

Step-to-Step Explanation:

1.

(a)Decay

(b)
`y=a(1-r)^(x)`

r = rate of decay, a is the initial value

1-r=0.57 = r=1-0.57 = r = 0.43

(c) a = 35

(d)
`y=35(0.57)^(3)\\\\y=35(0.185193)\\y=6.481755`

2.

(a) Growth

(b)
`y=a(1+r)^(x) \\`

r = rate of growth, a is the initial value

1+r=1.23 = r=1+1.23 = r = 2.23

(c) a = 225

(d)
`y=225(1.23)^(2) \\y=225(1.5129)\\y=340.4025`

Answer 2

Problem 1

Set the base of the exponent equal to 1+r and solve for r.

1+r = 0.57

r = 0.57-1

r = -0.43

The result is negative, which tells us we have exponential decay. Notice that b = 0.57 fits the interval 0 < b < 1.

The rate of decay is 43%

The initial value is a = 35 since this is the first value mentioned in the equation. Plugging x = 0 into the equation will lead to y = 35.

Let's now plug in x = 3

y = 35*(0.57)^x

y = 35*(0.57)^3

y = 35*0.185193

y = 6.481755

-----------------------------

Answers in bold:

• 1a. Decay
• 1b. 43% decay rate
• 1c. 35
• 1d. 6.481755

======================================================

Problem 2

We'll follow similar steps as problem 1.

1+r = 1.23

r = 1.23-1

r = 0.23

The r value is positive, so we have growth this time. Notice that b = 1.23 fits the interval b > 1.

The growth rate is 23% since r = 0.23 converts to this.

The initial value is a = 225. Compare y = a(1+r)^x to y = 225(1.23)^x to see how the terms match up. If you want you can think of it like y = 225(1+0.23)^x. Plugging x = 0 into the equation will lead to y = 225.

Let's plug in x = 2.

y = 225*(1.23)^x

y = 225*(1.23)^2

y = 225*1.5129

y = 340.4025

-----------------------------

Answers in bold:

• 2a. Growth
• 2b. Growth rate is 23%
• 2c. 225
• 2d. 340.4025