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Jawablah menggunakan rumus fungsi pertumbuhan eksponen yaitu y=k.a^x atau y=k. (1+r)^x

Let's work through the questions using the exponential growth formula \( y = k \cdot (1 + r)^x \), where:
- \( y \) is the final amount,
- \( k \) is the initial amount,
- \( r \) is the growth rate per period,
- \( x \) is the number of periods.

### Problem 1:
A virus doubles every 4 hours. After 12 hours, we need to find the total number of viruses if initially there are 200 viruses.

The growth factor is \( 2 \), and the initial amount is \( k = 200 \). In 12 hours, the virus doubles 3 times (since \( \frac{12}{4} = 3 \)).

\[
y = 200 \cdot 2^3 = 200 \cdot 8 = 1600
\]

**Answer for Problem 1:** After 12 hours, there will be 1600 viruses.

---

### Problem 2:
A farmer records a 10% increase in harvest yield every year, starting with 10 tons in the first year. We need to determine the harvest in the fourth year.

The initial harvest \( k = 10 \) tons, and the growth rate \( r = 10\% = 0.1 \). We need to find the harvest after 3 years of growth:

\[
y = 10 \cdot (1 + 0.1)^3 = 10 \cdot (1.1)^3
\]

Calculating \( (1.1)^3 \):

\[
(1.1)^3 \approx 1.331
\]

\[
y \approx 10 \cdot 1.331 = 13.31 \, \text{tons}
\]

**Answer for Problem 2:** The harvest in the fourth year will be approximately 13.31 tons.

---

### Problem 3:
Mrs. Dewi deposits Rp5,000,000 in a bank with an annual interest rate of 10%. We need to find the total amount after 6 years if she does not withdraw any money.

The initial deposit \( k = 5,000,000 \), the interest rate \( r = 10\% = 0.1 \), and the number of years \( x = 6 \).

\[
y = 5,000,000 \cdot (1 + 0.1)^6 = 5,000,000 \cdot (1.1)^6
\]

Calculating \( (1.1)^6 \):

\[
(1.1)^6 \approx 1.771561
\]

\[
y \approx 5,000,000 \cdot 1.771561 = 8,857,805
\]

**Answer for Problem 3:** After 6 years, Mrs. Dewi will have approximately Rp8,857,805 in the bank.

---

### Do you have any questions or would you like further details on any of the solutions?

Here are 5 related questions for further practice:
1. How many viruses will there be after 24 hours in Problem 1?
2. What is the harvest in the fifth year for Problem 2 if the growth continues at the same rate?
3. If the interest rate for Mrs. Dewi's bank account increases to 12%, what would the amount be after 6 years?
4. In Problem 2, what would the harvest be after 10 years with the same growth rate?
5. How much interest does Mrs. Dewi earn after 6 years with a 10% interest rate?

**Tip:** In exponential growth problems, doubling time or growth rates are key factors that can be easily calculated using logarithms or powers.

A virus doubles every 4 hours. After 12 hours, how many viruses will there be if initially there are 200 viruses? A farmer records an annual harvest increase of 10% for 10 years, starting with 10 tons. What is the harvest in the fourth year? Mrs. Dewi deposits Rp5,000,000 in a bank with an annual interest of 10%. What will her savings be after 6 years?

Solve real-life problems using the exponential growth formula. Learn how to calculate the number of viruses after 12 hours, the harvest in the fourth year with a 10% annual increase, and Mrs. Dewi's bank savings after 6 years with 10% interest. Suitable for students in Grades 9-11.

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