The problem describes an exponential growth model, where the future price $p(t)$ of an item is given by:

$p(t) = 1500 \cdot (1.039)^t$

1. Finding the Current Price ($t = 0$):

Substitute $t = 0$ into the equation:

$p(0) = 1500 \cdot (1.039)^0 = 1500 \cdot 1 = 1500$

The current price of the item is $1500.

2. Finding the Price 10 Years From Today ($t = 10$):

Substitute $t = 10$ into the equation:

$p(10) = 1500 \cdot (1.039)^{10}$

First, calculate $(1.039)^{10}$:

$(1.039)^{10} \approx 1.456$

Then:

$p(10) = 1500 \cdot 1.456 \approx 2184$

The price 10 years from today is approximately $2184.

Final Answers:

• Current Price: $1500
• Price in 10 Years: $2184

Would you like further details or a step-by-step breakdown of the calculations?

Related Questions:

1. How is exponential growth different from linear growth in pricing models?
2. What would the price be 20 years from today using this model?
3. How sensitive is this model to changes in the inflation rate?
4. Could a compound interest formula explain the same concept here?
5. What assumptions does this model make about inflation?

Tip: For exponential functions, small increases in the growth rate significantly impact long-term projections.