State whether each situation is best represented by an exponential or linear function. Then write an exponential or linear function for the model and state whether the model is increasing or decreasing. 1. Enrollment at a school is initially 454 students and grows by 3% per year. A salesperson initially earns $50,434 dollars per year and receives a yearly raise of $675. 2. 3. A customer borrows $450 at 5% interest compounded annually. 4. A wildlife park has 35 zebras and sends 1 zebra to another wildlife park each year.
State whether each situation is best represented by an exponential or linear function. Then write an exponential or linear function for the model and state whether the model is increasing or decreasing. 1. Enrollment at a school is initially 454 students and grows by 3% per year. A salesperson initially earns $50,434 dollars per year and receives a yearly raise of $675. 2. 3. A customer borrows $450 at 5% interest compounded annually. 4. A wildlife park has 35 zebras and sends 1 zebra to another wildlife park each year.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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State whether each situation is best represented by an exponential
or linear function. Then write an exponential or linear function for
the model and state whether the model is increasing or decreasing.
1.
Enrollment at a school is initially 454 students and grows by 3% per year.
A salesperson initially earns $50,434 dollars per year and receives a yearly raise
of $675.
2.
3.
A customer borrows $450 at 5% interest compounded annually.
4.
A wildlife park has 35 zebras and sends 1 zebra to another wildlife park each
year.
5. The value of a house is $546,768 and decreases by 3% each year.
6.
The population of a town is 66,666 people and decreases by 160 people each year.
7.
A business has a total income of $236,000 and revenues go up by 6.4% per year.
Expert Solution
Step 1
(1) Enrollment at school is initially 454 students and grows by per year.
Formula:
Next value
The data table is:
| (year) | (students) |
| 0 | 454 |
| 1 | 467.62 |
| 2 | 481.6486 |
| 3 | 496.098058 |
| 4 | 510.98099974 |
| 5 | 526.310429732 |
Since, ,
(a) It is clear that the change is not linear. Therefore, this situation represents an exponential function.
(b) We know that an exponential function is given by , where
Here, and
Therefore,
The equation for the model is
(c) The model is increasing.
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