Given that $p$ is directly proportional to ${{\left( q+1 \right)}^{2}}$ and that the differ

Question

Given that $p$ is directly proportional to ${{\left( q+1 \right)}^{2}}$ and that the difference between the value of $p$ when $q=2$ and $q=6$ is $80$. Express $p$ in terms of $q$. Hence, find the value of $p$ when $q=3$. Source check: the stated difference does not specify its order or the sign of $p$. Both signs of the proportionality constant are possible; the positive answer assumes $p(6)-p(2)=80$.

Accepted Answer

(a) $p=\pm2(q+1)^2$. (b) Correspondingly, $p=\pm32$. The positive case assumes $p(6)-p(2)=80$.

Direct Proportion Involving a Squared Expression

Direct Proportion Involving a Squared Expression

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