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The problem in the image asks how long it will take for the world population to double if it increases by 2% per year. This is a classic question involving exponential growth.

### Solution:
We can solve this using the formula for exponential growth:

\[
P(t) = P_0 (1 + r)^t
\]

Where:
- \( P(t) \) is the population after time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the annual growth rate (in decimal form), and
- \( t \) is the number of years.

In this case, the population doubles, so \( P(t) = 2P_0 \), and the growth rate is 2%, or \( r = 0.02 \). Substituting these into the formula:

\[
2P_0 = P_0 (1 + 0.02)^t
\]

We can cancel out \( P_0 \) on both sides:

\[
2 = (1.02)^t
\]

Now, take the natural logarithm (ln) of both sides to solve for \( t \):

\[
\ln(2) = t \ln(1.02)
\]

\[
t = \frac{\ln(2)}{\ln(1.02)}
\]

Now, let's compute the value of \( t \).

\[
\ln(2) \approx 0.6931 \quad \text{and} \quad \ln(1.02) \approx 0.0198
\]

Thus:

\[
t = \frac{0.6931}{0.0198} \approx 35
\]

### Conclusion:
It will take approximately **35 years** for the population to double if it increases by 2% per year.

Would you like further details or have any questions?

Here are five related questions:
1. How would the time change if the growth rate was 3% instead of 2%?
2. What is the formula for compound interest, and how does it relate to this problem?
3. How can you calculate the tripling time of a population with a similar growth rate?
4. Can you solve for the time to double using the rule of 70 instead of logarithms?
5. What are some real-world factors that might cause population growth to deviate from a constant 2% rate?

**Tip**: The "Rule of 70" is a quick way to estimate doubling time: divide 70 by the growth rate (as a percentage).

Si la population mondiale augmente de 2% par an, combien faudra-t-il d'années pour que la population double?

Find out how to calculate the time it takes for the world population to double with a 2% annual growth rate. This problem involves exponential growth concepts and logarithmic functions, perfect for students in Grades 10-12.

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