To determine the initial value and the rate of change for Joshua's new tomato plant, we can interpret the provided information as follows:
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Initial Value (b): This represents the starting height of the tomato plant. Since the height of the plant today is given as 10 inches, we can take this as our initial value. Hence, \( b = 10 \) inches.
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Rate of Change (m): This refers to how much the height of the plant increases each day. The problem states that the plant grows 1.7 inches each day. Thus, the rate of change is \( m = 1.7 \) inches per day.
In summary:
- The initial value is \( b = 10 \) inches.
- The rate of change is \( m = 1.7 \) inches per day.