At the beginning of the year, the number of books owned by a library was 10,000. Since then, it has grown by 1% each month. Which expressions represent the number of books, in thousands, owned by the library 5 years later if it continues to grow at that rate?

y = 10(1.01)^60

Step-by-step explanation:

The general equation of exponential growth is

y = ab^x

b has to do with the rate of growth.

b = 1 + r, so in this case, b = 1 + 1% = 1 + 0.01 = 1.01.

Now we have

y = a(1.01)^x

a is the initial value, so now we have

y = 10000(1.01)^x

where y is the number of books after x months

Since you need the number of books after 5 years, we must convert 5 years into months.

5 years * (12 months)/year = 60 months

The problem wants the expression in thousands of books, so we divide the initial value by 1000.

y = 10(1.01)^60

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