$p$ is directly proportional to $t$.
\[
p=48 \text { when } t=8
\]
a) Use the information above to write an equation for $p$ in terms of $t$.
b) What is the value of $p$ when $t=14 ?$
Give any decimal answers to 1 d.p.
Answer
\(\boxed{\text{b) } p = 84}\)
Step 1 ：Given that p is directly proportional to t, we can write the equation as p = kt, where k is the constant of proportionality.
Step 2 ：Using the given information, p = 48 when t = 8, we can find the value of k: \(48 = k \times 8\)
Step 3 ：Solving for k, we get \(k = \frac{48}{8} = 6\)
Step 4 ：Now we can write the equation for p in terms of t: \(p = 6t\)
Step 5 ：\(\boxed{\text{a) } p = 6t}\)
Step 6 ：To find the value of p when t = 14, we can substitute t = 14 into the equation: \(p = 6 \times 14\)
Step 7 ：Calculating the value of p, we get \(p = 84\)
Step 8 ：\(\boxed{\text{b) } p = 84}\)
