1.29: Estimate roots using a graph

4PM1/2/June/2021 — Question 7 · 9 marks

(a) Complete the table of values for

y = 3^{\frac{x}{4}} + 2

Give your answers to 2 decimal places where appropriate.

$x$	$0$	$1$	$2$	$3$	$4$	$5$
$y$	$3$	$3.32$				$5.95$

(2)

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

y = 3^{\frac{x}{4}} + 2 \quad \text{for} \quad 0 \leq x \leq 5

(2)

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

\mathrm{log}_{3}(6-2x)^4 - x = 0

in the interval

0 \leq x \leq 5

(5)