Question

In 2010, a total of 2187 of the employees

at Leo's company owned a petrol car.
In 2013, there were 1536 employees with
petrol cars.
Assuming this number decreases
exponentially, work out how many
employees owned a petrol car in 2019.
Give your answer to the nearest integer.

Answer 1

We can use exponential decay formula to solve this problem:

N(t) = N0 * e^(-kt)

where N(t) is the number of employees with petrol cars at time t, N0 is the initial number of employees with petrol cars (in 2013), k is the decay constant, and e is the base of the natural logarithm.

We need to find N(2019), the number of employees with petrol cars in 2019. We know that N0 = 1536, and we need to find k.

Let's assume that the number of employees with petrol cars decreases by 5% each year. This means that the ratio of the number of employees with petrol cars in two consecutive years is:

0.95

Therefore, we can write:

N(2019) = 1536 * 0.95^(2019-2013)

N(2019) = 1536 * 0.95^6

N(2019) = 1133.76

Rounding to the nearest integer, we get:

N(2019) = 1134

Therefore, we can estimate that about 1134 employees owned a petrol car in 2019, assuming that the number of employees with petrol cars decreases exponentially at a rate of 5% per year.