1.2: Complete the table of values for y = 1 + 3e⁻ˣ

4PM1/1/June/2022 — Question 6 · 11 marks

(a) Complete the table of values for

y = 1 + 3\mathrm{e}^{-x}

giving your answers to 2 decimal places where appropriate.

$\displaystyle x$	$\displaystyle 0$	$\displaystyle 0.25$	$\displaystyle 0.5$	$\displaystyle 1$	$\displaystyle 1.5$	$\displaystyle 2$	$\displaystyle 3$
$\displaystyle y$		$\displaystyle 3.34$	$\displaystyle 2.82$		$\displaystyle 1.67$		$\displaystyle 1.15$

(2)

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

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

(2)

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

x = \mathrm{e}^{-x} \quad \text{in the interval} \quad 0 \leq x \leq 3

(3)

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

\mathrm{ln}\,(x-1)^3 = -3x \quad \text{in the interval} \quad 0 \leq x \leq 3

(4)