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.
To find the ratio of the number of skin cancer deaths from year to year, we can divide the number of deaths in one year by the number of deaths in the previous year.
Let's first calculate the ratio of the number of deaths between 2001 and 2000:
Number of deaths in 2000 = 9,300
Number of deaths in 2001 = 9,300 * ratio
Since the number of deaths increases geometrically, the growth factor ratio can be derived by dividing the number of deaths in 2050 by the number of deaths in 2000:
2050 deaths = 200,000
2000 deaths = 9,300
Therefore, the growth factor ratio is:
ratio = (2050 deaths) / (2000 deaths)
ratio ≈ 200,000 / 9,300 ≈ 21.51
So, the ratio of the number of deaths from year to year is approximately 21.51.
To find the ratio of the number of deaths from year to year, we need to determine the common ratio of the geometric sequence.
In a geometric sequence, each term is obtained by multiplying the previous term by a constant factor called the common ratio (r).
Given that the number of skin cancer deaths increases geometrically, we can write the sequence as follows:
2000: 9,300 (the starting number)
2050: 200,000
To find the common ratio (r), we can divide any term by the previous term. Let's divide the 2050 number by the 2000 number:
r = 200,000 / 9,300 = 21.505376344086022
Now that we have determined the common ratio (r), we can find the number closest to the ratio of the number of deaths from year to year. We will consider the ratio between consecutive years, such as the ratio from 2000 to 2001, 2001 to 2002, and so on.
For example, to find the ratio of deaths from 2000 to 2001, we need to multiply the number of deaths in 2000 by the common ratio (r):
2000 to 2001: 9,300 * r = 9,300 * 21.505376344086022 = 200,000
Similarly, we can find the ratios for the subsequent years using the same formula.
Unfortunately, without more information on the annual number of skin cancer deaths for specific years, it is not possible to determine the number closest to the ratio of deaths from year to year. The calculations can only be made if the annual number of deaths is known for each year.