The table of values below is for the curve $y = 2^x - 3$. $x$$-1$$-0.5$$0$$0.5$$1$\(1.

Question

The table of values below is for the curve $y = 2^x - 3$. $x$$-1$$-0.5$$0$$0.5$$1$$1.5$$2$$2.5$$3$ $y$$-2.5$$-2.3$$p$$-1.6$$-1$$-0.2$$1$$2.7$$5$ Find the value of $p$. Using a scale of $4$ cm to represent $1$ unit on the horizontal $x$-axis and $2$ cm to represent $1$ unit on the vertical $y$-axis, draw the graph of $y = 2^x - 3$ for $-1 \le x \le 3$. Use your graph to find the value of $x$ when $y = 3.5$, the gradient of the curve at $x = 2$. On the same graph, draw the line $y = -x$. Hence, find the solution to the equation $2^x - 3 = -x$.

Accepted Answer

(a) $-2$ (c)(i) $27$ (ii) $2.76\left( \pm 0.1 \right)$ (d)(ii) $1$

Functions

Functions