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 or Non-Linear.
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
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.)
Using MS-Excel, which forest’s population is growing at a faster rate?
Which forest had a greater number of trees initially? By how many?
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?
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?
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?
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.
The population of a city is modeled by the equation P(t) = 256,114e0.25t where t is 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?
