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The problem is asking to find the smallest number of years after which a laptop computer, initially purchased for $1500, will be worth $300 or less, given that its value decreases by 70% each year (or retains 70% of its previous value).

This is a typical exponential decay problem, where the value $ V $ of the laptop after $ t $ years is given by the equation:

\[
V(t) = 1500 \times (0.70)^t
\]

We need to determine the smallest $ t $ such that:

\[
V(t) \leq 300
\]

Let's solve this equation:

\[
1500 \times (0.70)^t \leq 300
\]

Dividing both sides by 1500:

\[
(0.70)^t \leq \frac{300}{1500} = 0.2
\]

Now, we solve for $ t $ by taking the logarithm of both sides:

\[
\log(0.70^t) \leq \log(0.2)
\]

Using the logarithmic property $ \log(a^b) = b \log(a) $:

\[
t \log(0.70) \leq \log(0.2)
\]

Finally, solving for $ t $:

\[
t \geq \frac{\log(0.2)}{\log(0.70)}
\]

Let's calculate this.The smallest number of years after which the laptop's value will be $300 or less is approximately 4.51 years. Since we need the smallest whole number, the answer is **5 years**.

Would you like more details or have any questions about this solution?

Here are 5 related questions:
1. How do exponential decay models apply in real-world scenarios?
2. What happens if the decay rate is less than 70%? How would the answer change?
3. How can logarithms help solve exponential equations?
4. Can this method be used for other depreciating assets like cars or phones?
5. What is the effect of compounding depreciation annually versus monthly?

**Tip:** In exponential decay, the value decreases faster at first, then the rate of decrease slows down as time passes.

A laptop computer is purchased for $1500. Each year, its value is 70% of its value the year before. After how many years will the laptop computer be worth $300 or less?

Learn how to solve an exponential decay problem where the value of a laptop decreases by 70% each year. This detailed solution shows how to calculate after how many years the laptop's value will fall to $300 or less using logarithms and exponential formulas. Suitable for students in Grades 9-12.

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