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Are there maximum and minimum values for the exponential function y = 100 (0.85) t , 0 ≤ 6. Explain?

Yes, there are maximum and minimum values for the exponential function

$$y = 100 (0.85)^t , \quad 0 \leq t \leq 6.$$

The function is decreasing because the base of the exponential function, 0.85, is less than 1. The function starts at 100 when \( t = 0 \) and decreases as \( t \) increases. The function will approach but never reach 0 as \( t \rightarrow \infty \).

Therefore, the maximum value is \( y = 100 \) when \( t = 0 \), and the minimum value is \( y \approx 29.75 \) when \( t = 6 \).

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