Assume the annual number of skin cancer deaths increases geometrically. Use the starting number of 9,300 in 2000 and 200,000 in 2050.

Select the number closest to the ratio of number of deaths from year to year.
a) 1.0633
b) 1.3259
c) 1.6320
d) 1.0655

Question

Assume the annual number of skin cancer deaths increases geometrically. Use the starting number of 9,300 in 2000 and 200,000 in 2050.

Select the number closest to the ratio of number of deaths from year to year.
a) 1.0633
b) 1.3259
c) 1.6320
d) 1.0655

whpalmer4 · Answer

This is just saying that

$$9300*a^{50} = 200000$$and asking you to find the value of $a$

I'm suspicious that one of the answer choices has a typo...

anonymous · Answer

Oops! I did mess up on the first answer choice! I'm sorry!

whpalmer4 · Answer

Actually, I was looking at a different one!

whpalmer4 · Answer

Do you know how to solve for $a$ in that equation?

anonymous · Answer

Yes! I got a! Is that correct??:)))

whpalmer4 · Answer

Yes, $1.0633^50 = 21.5174$ and $21.5174*9300 = 200112$ so that appears to be correct!

whpalmer4 · Answer

Oops, I forgot the { } around the exponent.  Should have been 
$$1.0633^{50} = 21.5174$$

anonymous · Answer

Okay, so, 2 questions later, it says "Compare the total number of deaths due to skin cancer expected between 2000 and 2050, if the progression were geometric and if the progression were arithmetic." 
Is there a formula for that that i forgot to take note of?  The question means like every single year added up, for 50 years. D:

anonymous · Answer

Yay, thank you!

anonymous · Answer

Like, i know the formulas for just one year, specifically, but, gahh, 50 together??

whpalmer4 · Answer

It's not entirely clear to me what the arithmetic progression would be, I'm sorry to say

But the sum of an arithmetic progression isn't difficult to find.  And no, you don't have to add up each term by hand :-)

whpalmer4 · Answer

If you have an arithmetic sequence $a_1,a_2,a_3,...$, and you want to add the first $n$ terms, it's just 
$$S_n = \frac{n(a_n+a_1)}{2}$$

anonymous · Answer

What are 'an' and 'a1' again? 
i need to make sure i plugged it in right, 'cause my answer is really close to one listed but not quite..

whpalmer4 · Answer

$a_1$ is the first term
$a_n$ is the $n$th term

anonymous · Answer

Yeah, i'm getting 5,232,500 by plugging in 50 for n, 200,000 for the 50th term, and 9300 for the first term. The closest choice is 5,223,200. Am i doing something wrong? :(

anonymous · Answer

@whpalmer4  :(

whpalmer4 · Answer

Here's a hint: why don't you subtract your answer from the closest choice (or the other way around).

anonymous · Answer

i meat to post this last night but my internet turns off at midnight! 
After subtracting my answer from the closest choice, i got the starting amount! So, i picked that answer. :) haha 
Thank you soooo sosososososo much for your help!!