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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.

The provided problems include (1) virus reproduction, (2) harvest growth over 10 years, and (3) calculating compound interest on savings.

Solve exponential growth, percentage increase, and compound interest problems, including virus reproduction, harvest yield growth, and calculating savings interest. Learn how to apply key formulas like y = k * (1 + r)^x and A = P(1 + r)^t to real-world scenarios.

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