topic badge
AustraliaVIC
VCE 11 General 2023

5.06 Applications of geometric sequences

Interactive practice questions

For the following table, compute the mass of $800$800 grams of radioactive element $D$D left each day if element $D$D loses half its mass every day.

a
Day Mass of radioactive element $D$D (g)
$0$0 $800$800
$1$1 $\editable{}$
$2$2 $\editable{}$
$3$3 $\editable{}$
$4$4 $\editable{}$
b

What type of decay is this?

Linear decay

A

Exponential decay

B
Easy
< 1min

Suppose you save $\$1$$1 the first day of a month, $\$2$$2 the second day, $\$4$$4 the third day, $\$8$$8 the fourth day, and so on. That is, each day you save twice as much as you did the day before.

Easy
2min

Suppose you save $\$1$$1 the first day of a month, $\$2$$2 the second day, $\$4$$4 the third day, $\$8$$8 the fourth day, and so on. That is, each day you save twice as much as you did the day before.

Easy
4min

A car enthusiast purchases a vintage car for $\$220000$$220000. Each year, its value increases at a rate of $12$12 percent of its value at the beginning of the year. Find its value after $7$7 years, to two decimal places.

Easy
2min
Sign up to access Practice Questions
Get full access to our content with a Mathspace account

Outcomes

U1.AoS2.5

the use of first-order linear recurrence relations of the form u_o=a,u_{n+1}=RU_nwhere 𝑎 and 𝑅 are constants to model compound interest investments and loans, reducing balance depreciation of an asset over time, including the rule for the future value of the asset after 𝑛 depreciation periods, compound interest investments and debts

U1.AoS2.7

use a given recurrence relation to generate a sequence, deduce the explicit rule, n u from the recursion relation, tabulate, graph and evaluate the sequence

U1.AoS2.9

demonstrate the use of a recurrence relation to determine the linear depreciating value of an asset after 𝑛 time periods for the initial sequence

U1.AoS2.10

use a rule for the future value of a linear depreciating asset to solve practical problems

What is Mathspace

About Mathspace