Reference no: EM132395176
Assignment
For the following exercises, enter the data from each table into MS-Excel and graph the resulting scatter plots (Use a smoothing function). Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic.
|
n
|
1.25
|
2.25
|
3.56
|
4.2
|
5.65
|
6.75
|
7.25
|
8.6
|
9.25
|
10.5
|
|
f (n)
|
5.75
|
8.75
|
12.68
|
14.6
|
18.95
|
22.25
|
23.75
|
27.8
|
29.75
|
33.5
|
|
x
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
f (x)
|
2
|
4.079
|
5.296
|
6.159
|
6.828
|
7.375
|
7.838
|
8.238
|
8.592
|
8.908
|
|
m
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
10
|
|
F(m)
|
10
|
12
|
14
|
16
|
18
|
20
|
22
|
24
|
26
|
28
|
|
y
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
|
f (y)
|
2.4
|
2.88
|
3.456
|
4.147
|
4.977
|
5.972
|
7.166
|
8.6
|
10.32
|
12.383
|
|
z
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
|
f (z)
|
9.429
|
9.972
|
10.415
|
10.79
|
11.115
|
11.401
|
11.657
|
11.889
|
12.101
|
12.295
|
2. For the following exercises, consider this scenario: For each year t, the population of a forest of trees is represented by the function A(t) = 115(1.025)t. In a neighboring forest, the population of the same type of tree is represented by the function B(t) = 82(1.029)t. (Round answers to the nearest whole number.)
a. Using MS-Excel, which forest's population is growing at a faster rate?
b. Which forest had a greater number of trees initially? By how many?
c. Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 20 years? By how many?
d. Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 50 years? By how many?
3. An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
4. Drew wants to save $2,500 to go to the next World Cup. To the nearest dollar, how much will he need to invest in an account now with 6.25% APR, compounding daily, in order to reach his goal in 4 years.
5. The population of a city is modeled by the equation P(t) = 256,114e0.25twhere tis measured in years. If the city continues to grow at this rate, how many years will it take for the population to reach one million?