Assume the annual number of skin cancer deaths increases geometrically, instead of arithmetically. Use the same 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.
fifty years?
P(50)=P(0)a^50
200000=9300*a^50
take log of both sides
log(200,000)=log(9300)+50log(a)
50log(a)=log(200,000)-log(9300) =log(200,000/9300)=1.333
log(a)= 0.0266509409
a= 10^ 0.0266509409=1.064
checkP(50)=9300(1.064)^50=206806.577
To find the ratio of the number of skin cancer deaths from year to year, we need to calculate the annual growth factor between each year.
First, we need to find the number of years between 2000 and 2050 as follows:
Number of years = 2050 - 2000 = 50 years
Next, we can calculate the growth factor using the formula:
Growth factor = (Final value / Initial value) ^ (1 / number of years)
Now, let's substitute the given values into the formula:
Initial value = 9,300
Final value = 200,000
Number of years = 50
Growth factor = (200,000 / 9,300) ^ (1 / 50)
To find the ratio of the number of deaths from year to year, we can calculate the successive quotients between each year starting from 2000. We will also round the ratios to the nearest whole number to find the closest value:
Year 2000 to 2001: Growth factor = (Final value in 2001 / Initial value in 2000) rounded to the nearest whole number
Year 2001 to 2002: Growth factor = (Final value in 2002 / Final value in 2001) rounded to the nearest whole number
Year 2002 to 2003: Growth factor = (Final value in 2003 / Final value in 2002) rounded to the nearest whole number
...
Year 2049 to 2050: Growth factor = (Final value in 2050 / Final value in 2049) rounded to the nearest whole number
By calculating the above ratios for each year, we can determine the number closest to the ratio of the number of deaths from year to year.