Variables $x$ and $y$ are related by the equation $y=1-{{2}^{x}}$. Some corresponding values o

Question

Variables $x$ and $y$ are related by the equation $y=1-{{2}^{x}}$. Some corresponding values of $x$ and $y$ are given in the following table. $x$ $-2$ $-1$ $0$ $0.5$ $1$ $1.5$ $2$ $2.5$ $y$ $0.75$ $0.5$ $0$ $-0.4$ $-1$ $-1.8$ $-3$ $p$ Using a scale of $4$ cm to represent $1$ unit on the $x$-axis, and $2$ cm to represent $1$ unit on the $y$-axis. Draw the graph of $y=1-{{2}^{x}}$ for $-2\le x\le 2.5$. Use the graph and solve the equation ${{2}^{x}}=5$. By drawing a tangent at the point where $x=2$, find the gradient of the curve at the point $\left( 2,-3 \right)$. Solve the equation ${{2}^{x}}+2x-2=0$.

Accepted Answer

(a) $p=-4.66$. (b) $x\approx2.3$. (c) Gradient $\approx-2.73$. (d) $x\approx0.35$.

Exploring Exponential Graphs and Their Applications

Exploring Exponential Graphs and Their Applications

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