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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?

Respuesta :

mathstudent55

Answer:

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.

Answer: y = 10(1.01)^60

   Expression representing the number of books after 5 years,              

                           [tex]A(60)=10000(1.01)^{60}[/tex]

Exponential growth:

  •  Exponential growth function is given by,

          [tex]A(t)=A_0(1+r)^t[/tex]

          Here, [tex]A(t)=[/tex] Final amount

          [tex]A_0=[/tex] Initial amount

           [tex]r=[/tex] Growth rate

           [tex]t=[/tex] Duration or time

Given in the question,

  • Initial number of books = 10000
  • Growth rate = 1%
  • Duration = 5 years ≈ 60 months

Substitute these values in the expression,

[tex]A(t)=A_0(1+r)^t[/tex]

[tex]A(60)=10000(1+0.01)^{60}[/tex]

      Therefore, expression representing the number of books after 5 years will be → [tex]A(60)=10000(1.01)^{60}[/tex]

Learn more about the exponential growth here,

https://brainly.com/question/10709151?referrer=searchResults