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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 10,000 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%, percent every 6 months.

Respuesta :

MrRoyal

Answer:

5842 people after 2 months

Step-by-step explanation:

Given

Initial Value: [tex]a =10000[/tex]

Rate: [tex]r = 20\%[/tex] every 6 months

Required

Number of people using it after 2 months

The function follows an exponential model.

So, we need to first write out the function.

If Rate: [tex]r = 20\%[/tex] every 6 months

Then

Rate: [tex]r = 40\%[/tex] after 1 year

[tex]r = 0.04[/tex]

The function is represented as:

[tex]y = ar^x[/tex]

So:

[tex]y = 10000 * 0.04^t[/tex]

For 2 months, we have:

[tex]t = 2\ months[/tex]

Convert to years

[tex]t = \frac{2}{12}[/tex]

[tex]t = 0.167[/tex]

[tex]y = 10000 * 0.04^t[/tex]

[tex]y = 10000 * 0.04^{0.167}[/tex]

[tex]y = 5842[/tex]