1.5: Complete the table of values for y = e³ˣ⁻²

4PM1/2R/June/2022 — Question 5 · 7 marks

(a) Complete the table of values for

y = \mathrm{e}^{3x-2}

giving your answers to 2 decimal places.

$\displaystyle x$	$\displaystyle 0$	$\displaystyle 0.25$	$\displaystyle 0.5$	$\displaystyle 0.75$	$\displaystyle 1$
$\displaystyle y$	$\displaystyle 0.14$				$\displaystyle 2.72$

(2)

(b) On the grid opposite, draw the graph of

y = \mathrm{e}^{3x-2} \quad \text{for} \quad 0 \leq x \leq 1

(2)

(c) By drawing a suitable straight line on the grid, obtain an estimate, to one decimal place, of the root of the equation

3x = 2 + \mathrm{ln}\,(3-x)

(3)