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Let's solve each problem shown in the image.

### Problem 1
**Question:** The current population of a city is estimated to be 77,435 people. Assume the city population grows by about 1.05% per year. Predict the city population 19 years from now. Round to the nearest whole number.

**Solution:**
To solve this, we use the formula for exponential growth:
\[
P = P_0 \times (1 + r)^t
\]
Where:
- \( P_0 = 77,435 \) (initial population)
- \( r = 0.0105 \) (annual growth rate)
- \( t = 19 \) years

\[
P = 77,435 \times (1 + 0.0105)^{19}
\]
\[
P = 77,435 \times (1.0105)^{19}
\]

Calculating \( (1.0105)^{19} \approx 1.2214 \):

\[
P \approx 77,435 \times 1.2214 \approx 94,570
\]

So, the population 19 years from now is approximately **94,570** people.

### Problem 2
**Question:** 16,830 people work in a particular occupation at the present time. The number of people working in the occupation is projected to decrease by 0.2% per year. If we assume that the decay rate remains at that level, how many people would we expect to work in that occupation in 18 years? Round to the nearest whole number.

**Solution:**
For decay, we use the formula:
\[
P = P_0 \times (1 - r)^t
\]
Where:
- \( P_0 = 16,830 \) (initial number of people)
- \( r = 0.002 \) (annual decay rate)
- \( t = 18 \) years

\[
P = 16,830 \times (1 - 0.002)^{18}
\]
\[
P = 16,830 \times (0.998)^{18}
\]

Calculating \( (0.998)^{18} \approx 0.964 \):

\[
P \approx 16,830 \times 0.964 \approx 16,223
\]

So, the number of people working in the occupation 18 years from now is approximately **16,223** people.

### Final Answers:
1. **94,570** people (population in 19 years).
2. **16,223** people (workers in 18 years).

Would you like more details or have any questions about these solutions?

### Expanded Questions:
1. How does changing the growth rate in the first problem affect the population in 19 years?
2. What would happen if the decay rate in the second problem was 0.5% instead of 0.2%?
3. Can you calculate the population 25 years from now using the same growth rate as in the first problem?
4. If the initial population in the first problem was higher (e.g., 100,000), how would that affect the future population?
5. How would you set up the equations if the population growth or decay rate changed every 5 years?

**Tip:** When solving exponential growth or decay problems, always verify if the rate is positive (growth) or negative (decay) to apply the correct formula.

The current population of a city is estimated to be 77,435 people. Assume the city population grows by about 1.05% per year. Predict the city population 19 years from now. Round to the nearest whole number.
16,830 people work in a particular occupation at the present time. The number of people working in the occupation is projected to decrease by 0.2% per year. If we assume that the decay rate remains at that level, how many people would we expect to work in that occupation in 18 years? Round to the nearest whole number.

This problem covers predicting city population growth (77,435 people with a 1.05% increase over 19 years) and occupational decay (16,830 people with a 0.2% decrease over 18 years). Learn the steps for solving exponential growth and decay problems, suitable for students in Grades 10-12.

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