The graph on the left shows the annual revenue growth rate of Company X. The graph on the right shows the tax rate as a percent of revenue for each year. If Company X's revenue in year ‘99 was $98.1 million, which one of the following is closest to how much more the company paid in taxes in year ‘01 than ‘00?

A. $4 million B. $6 million C. $13 million D. $15 million E. $20 million

(B) There are a few steps to solving this problem: First, given 1999 revenue of $98.1 million, we can find the revenue in 2000 and 2001 because the increase from 1999 to 2000 was 4% and the increase from 2000 to 2001 was 5% (Note: since the answer says “closest,” rounding can be done in the calculations): 1999: $98.1 million 2000: ($98.1)(1.04) = $102 million 2001: ($102)(1.05) = $107 million.

Now, given each year's revenue amounts, calculate the taxes paid: 2000: ($102)(0.20) = $20 million 2001: ($107)(0.25) = $27 million.

Now subtract the 2000 tax amount from the 2001 amount: $27 – $20 = $7 million.

Company X paid $7 million more in taxes in 2001 than it did in 2000. The closest answer is choice (B), which is the correct answer. ---------- Is this question correct? The explanation stated: "First, given 1999 revenue of $98.1 million, we can find the revenue in 2000 and 2001 because the increase from 1999 to 2000 was 4% and the increase from 2000 to 2001 was 5%".

However, the graph shows that the increase from 2000 to 2001 was 1%.

The graph shows that the revenue in 2001 grew by 1% more than it grew in 2000. Bu still in 2000 it grew 4% (comparing to 1999) and in 2001 it grew 5% (comparing to 2000).

Suppose the revenue in 1998 was Y. In 1999 it grew 2%: revenue in 1999 was 1.02Y. In 2000 it grew 4%: revenue in 2000 was 1.04 × (1.02Y). In 2001 it grew 5%: revenue in 2001 was 1.05 × 1.04 × (1.02Y).

Isn't the difference between the growth in 99' and the growth in 00' a difference of 2% instead of one of 4% as its suggested in the answer prompt? (because 99' is already at a level of 2% and 00' is at one of 4% so shouldn't the difference be 2%? Also should the diff. between 99' and 01' be 3%? instead of 5% as the answer prompt states? Thanks.

If it is not stated otherwise, the annual rate of growth shows how a quantity increased/decreased comparing to a PREVIOUS year, i.e. for 2000 it shows how a quantity in 2000 changed comparing to 1999, in 2001 - comparing to 2000, etc.

As you've mentioned, the difference between the growth RATE in 99' and the growth RATE in 00' is in fact 4% – 2% = 2%. But it doesn't give us anything in this question. While the difference between the REVENUE in 99' and the REVENUE in 00' is 4% of the REVENUE in 99' (as the graph shows). This allows us to compare the revenues, not the growth rates.

If the REVENUE in 1999 was S, then in 2000 the REVENUE was 1.04 × S, in 2001 the REVENUE was 1.05 × 1.04 × S.

So the difference between the REVENUE in 99' and 01' is: 1.05 × 1.04 × S – S = 1,092 × S, or 9.2% of the REVENUE in 99'.

The last paragraph should give you the full feeling of what the difference between the annual growth rate and growth rate compared to a certain year is.

If we rewrite the grow rate by year, COMPARING TO the revenue in 99' the numbers will be:

If we rewrite the grow rate by year, COMPARING TO the revenue in 00' the numbers will be:

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