A memory chip is being designed to hold a number of transistors and heat sinks. The transistors hold memory, while the heat sinks cool the chip. There must be at least one heat sink for every 2,000 transistors to prevent overheating. Also, each transistor has an area of 2.0×10⁻¹⁰mm² (square millimeters), each heat sink has an area of 3.6×10⁻⁶mm², and the total area of transistors and heat sinks must be at most 2mm². What is the approximate maximum number of transistors that the chip can hold according to this design?

To find the maximum number of transistors the chip can hold according to the given design constraints, we need to consider the area occupied by the transistors and heat sinks.

Given information:

- Area of each transistor = 2.0×10⁻¹⁰ mm²

- Area of each heat sink = 3.6×10⁻⁶ mm²

- Total area available for transistors and heat sinks = 2 mm²

- There must be at least one heat sink for every 2,000 transistors.

To determine the maximum number of transistors, we'll follow these steps:

1. Calculate the maximum number of heat sinks allowed based on the given total area available:

- Area of heat sinks = Total area available - Area of transistors

- Area of heat sinks = 2 mm² - (Number of transistors * Area of each transistor)

- Area of heat sinks = 2 mm² - (Number of transistors * 2.0×10⁻¹⁰ mm²)

2. Calculate the maximum number of transistors that can be accommodated by the remaining area allocated for heat sinks:

- Maximum number of heat sinks = Area of heat sinks / Area of each heat sink

- Maximum number of heat sinks = (2 mm² - (Number of transistors * 2.0×10⁻¹⁰ mm²)) / (3.6×10⁻⁶ mm²)

3. Calculate the maximum number of transistors:

- Number of transistors = Maximum number of heat sinks * 2,000

Let's substitute the given values into the equations:

Area of heat sinks = 2 mm² - (Number of transistors * 2.0×10⁻¹⁰ mm²)

Maximum number of heat sinks = (2 mm² - (Number of transistors * 2.0×10⁻¹⁰ mm²)) / (3.6×10⁻⁶ mm²)

Number of transistors = Maximum number of heat sinks * 2,000

By solving these equations, we can find the approximate maximum number of transistors the chip can hold according to this design.