QUESTION 1
iii
Easy
Suppose a plant has height 1.75 feet and it grows by 0.5 feet each month. Find an expression that relates h and t, and explain why it represents linear growth.
SOLUTION
A linear growth is represented by the general formula
\(h = h_{0} + (r × t)\)
From the given data, we have
\(h_{0} = 1.75\)
\(r = 0.5\)
Substituting these into the formula, we get
\(h = 1.75 + 0.5t\)
This expression represents linear growth because \(h\) increases by a fixed amount(\(0.5)\) for each unit increase in \(t\).
\(h = h_{0} + (r × t)\)
From the given data, we have
\(h_{0} = 1.75\)
\(r = 0.5\)
Substituting these into the formula, we get
\(h = 1.75 + 0.5t\)
This expression represents linear growth because \(h\) increases by a fixed amount(\(0.5)\) for each unit increase in \(t\).
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Final Answer :
\(h = 1.75 + 0.5t\)
Concept Note
Linear growth happens when a quantity increases by a fixed amount per unit of time. Its general form is
\(h = h_{0} + (r × t)\),
where
\(h = \) height after \(t\) months
\(h_{0} = \) initial height
\(r = \) constant increase
\(t = \) time in months