To find the demand function, we can define a few variables and use the information given.

1. Let $p$ represent the price of the tablet.
2. Let $q$ represent the quantity of tablets sold.

We know that:

• At a price of $350, the retailer sells 2000 tablets each week. So, $p = 350$ and $q = 2000$.
• For each $10 decrease in price, an additional 80 tablets are sold.

Step 1: Set up the linear relationship

We assume a linear demand function, which we can write as: $q = mp + b$ where $m$ is the slope and $b$ is the intercept.

Step 2: Determine the slope $m$

Since every $10 decrease in price results in an additional 80 tablets sold, we can use this to find $m$.

For a $10 decrease:

• Change in $p$: $-10$
• Change in $q$: $+80$

The slope $m$ is: $m = \frac{\Delta q}{\Delta p} = \frac{80}{-10} = -8$

Step 3: Substitute known values to find $b$

Now that we know $m = -8$, we can use the point $(p, q) = (350, 2000)$ to solve for $b$.

$2000 = -8(350) + b$ $2000 = -2800 + b$ $b = 4800$

Step 4: Write the demand function

The demand function is: $q = -8p + 4800$

Final Answer

The demand function is: $q = -8p + 4800$

Would you like a detailed explanation of any part of this solution?

Here are some related questions to explore further:

1. What is the inverse of the demand function, and how is it useful?
2. How would you calculate revenue based on the demand function?
3. How does elasticity of demand factor into this function?
4. What if the price increase rather than decrease? How does it impact the function?
5. Can we determine the price that maximizes revenue using this function?

Tip: To find revenue, multiply the demand function by price: $R = p \cdot q(p)$.