1.54: Logarithmic equations, exponential equations and graphical solution

(a) Complete the table of values for $y=e^{x-1}+2$. Give your answers to 2 decimal places where appropriate.

(b) On the grid opposite, draw the graph of $y=e^{x-1}+2$ for $-2\le x\le3$. (2)

(c) Use your graph to obtain an estimate, to 1 decimal place, of the root of the equation $4=e^{x-1}$ in the interval $-2\le x\le3$. (2)

(d) By drawing a straight line on the grid, obtain an estimate, to 1 decimal place, of the root of the equation $\ln(4x-4)=x-1$ in the interval $-2\le x\le3$. (5)