Question

The table shows the number of books donated to a library each month. The growth is exponential. Suppose the growth continues at the same rate.

How many books were donated to the library in Month 8?

Round to the nearest whole number.

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Answer 1

Is it 477?

Answer 2

or 380?

Answer 3

the common ratio, if you are learning series, is 1.25

Answer 4

80 x 1.25 -> 100 x 1.25 -> 125 and so on.

you can just keep that up or use a formulae, depends i suppose on what ya know :)

Answer 5

So I just multiply 1.25 by 8?

Answer 6

Sorry, I'm confused.

Answer 7

Solve for the rate first
rate = (ln [end ÷ bgn]) ÷ time

rate = (ln (100/80)/1
rate = (ln (10/8)/1
rate = 0.2231435513

Answer 8

\(80\cdot (1.25)^8 = 476.84\)

Answer 9

that agrees with you but you should understand why :)

Answer 10

So it's 476.84?

Answer 11

yes, but we're talking books here :)

so unless you rip out the right amount of pages you gotta round it

Answer 12

Then use this formula
end = bgn × e ^ rate*time
end = 80 * 2.71828^(0.2231435513*8)
end = 80 * 2.71828^(1.7851484105)
end = 80 * 5.9604644757
end = 476.8371580594

Answer 13

So it'd be 477 then?
Since you have to round, I guess.

Answer 14

super

but please do understand why

:-)

Answer 15

I do, thank you both.

Answer 16

u r welcome