The function $f(t) = 7000(1.025)^t$ describes the change in a quantity over time, with $t$ representing the number of weeks.

In this function, $7000$ is the initial value (the quantity at $t = 0$), and $1.025$ is the constant that plays a key role in determining the rate of change.

Interpretation of $1.025$:

• The constant $1.025$ is the growth factor.
• The rate of change is represented by the percentage increase each week, which can be found by subtracting 1 from $1.025$:
  $1.025 - 1 = 0.025 \text{ or } 2.5\%$ So, the quantity increases by 2.5% per week.

Conclusion:

The constant $1.025$ reveals that the quantity is growing at a rate of 2.5% per week.

Would you like more details or further explanation on this?

Here are 5 related questions to explore further:

1. How can I find the value of the quantity after a specific number of weeks?
2. What would happen if the constant was less than 1 (e.g., $1.015$)?
3. How do I determine the time $t$ when the quantity reaches a certain value?
4. Can this type of growth be used for other applications like population growth or finance?
5. What happens to the growth rate if the exponent $t$ is replaced with $2t$?

Tip: To convert a growth factor to a percentage rate, subtract 1 from the factor and multiply by 100.