Question
The value of a car is \( \$8000\).
Each year the value of the car decreases exponentially by $25\%$
Calculate the value of this car after $3$ years
▶️Answer/Explanation
$3375$
The formula for exponential depreciation is
$
V = P(1 – r)^t
$
\( V \) = value of the car after time
\( P = 8000 \) (initial value of the car)
\( r = 0.25 \) (the percentage decrease as a decimal)
\( t = 3 \) (time in years)
$
V = 8000(1 – 0.25)^3
$
$
= 8000(0.75)^3
$
$
= 8000(0.421875)
$
$
= 3375
$
Question
A town has a population of 45000.
This population increases exponentially at a rate of 1.6% per year.
Find the population of the town at the end of 5 years.
Give your answer correct to the nearest hundred.
………………………………………….
Answer/Explanation
48 700
Question
The population of the world grows exponentially at a rate of 1.1% per year.
Find the number of years it takes for the population to grow from 7 billion to 7.31 billion.
Give your answer correct to the nearest whole number.
……………………………………years
Answer/Explanation
Ans:
4 nfww
Question
In 1970 the population of China was $8.2 \times 10^8$. In 2007 the population of China was $1.322 \times 10^9$. Calculate the population in 2007 as a percentage of the population in 1970 .
▶️Answer/Explanation
161