Question

The number of people using an older version of a spreadsheet program decreases at a rate that is proportional at any time to the number of people still using the version at that time.

There were 10{,}00010,00010, comma, 000 people using the older version of the spreadsheet program when the new version first came out. The number of people still using the older version decreases by 20\%20%20, percent every 666 months.

Answer 1

The decrease in the use of older version is given by,
`y = 10000 \cdot0.60^(t)`.

Explanation:

It is provided that the number of people using an older version of a spreadsheet program decreases at a rate that is proportional at any time to the number of people still using the version at that time.

The exponential decay function is given as follows:

`y=a(1-r)^(t)`

Here,

y = final value

a = initial value

r = decay rate

t = time taken

It is provided that there were 10,000 people using the older version of the spreadsheet program when the new version first came out. And the number of people still using the older version decreases by 20% every 6 months.

So, every half-yearly the decrease in the number of people using the older version is 20%. This implies for a year the decay rate is 40%.

Then the decrease in the use of older version is given as follows:

`y=10000(1-0.40)^(t)\\\\y=10000\cdot 0.60^(t)`