Question
The exponential function given by
, where t is the number of years after 2008, can be used to project the number of
centenarians in a certain country. Use this function to project the centenarian population in this country in 2013 and in 2038 .
The centenarian population in 2013 is approximately
(Round to the nearest whole number.)
The centenarian population in 2038 is approximately
(Round to the nearest whole number.)
centenarians in a certain country. Use this function to project the centenarian population in this country in 2013 and in 2038 .
The centenarian population in 2013 is approximately
(Round to the nearest whole number.)
The centenarian population in 2038 is approximately
(Round to the nearest whole number.)
Ask by Estrada Harris. in the United States
Nov 12,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The centenarian population in 2013 is approximately 101,000.
The centenarian population in 2038 is approximately 343,000.
The centenarian population in 2038 is approximately 343,000.
Solution
To project the centenarian population using the function
, we need to determine the value of
for the years 2013 and 2038.
-
For the year 2013:
- The year 2013 is 5 years after 2008, so
. - Now we can substitute
into the function:
- First, calculate
:
- Now, substitute this value back into the equation:
- Rounding to the nearest whole number, the centenarian population in 2013 is approximately 101,000.
- The year 2013 is 5 years after 2008, so
-
For the year 2038:
- The year 2038 is 30 years after 2008, so
. - Now we can substitute
into the function:
- First, calculate
:
- Now, substitute this value back into the equation:
- Rounding to the nearest whole number, the centenarian population in 2038 is approximately 343,000.
- The year 2038 is 30 years after 2008, so
Summary:
- The centenarian population in 2013 is approximately 101,000.
- The centenarian population in 2038 is approximately 343,000.
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Beyond the Answer
To find the centenarian population using the function
, we substitute
with the number of years since 2008.
For 2013:
The value of is
.
The value of
Calculating
(you can use a calculator for precision),
Rounded to the nearest whole number, the centenarian population in 2013 is approximately 101,017.
For 2038:
The value of is
.
The value of
Calculating
,
Rounded to the nearest whole number, the centenarian population in 2038 is approximately 335,405.