Answer: 959
Explanation:
Step 1. The information that we have is:
The initial or actual amount of African cheetahs is 7,217, we will call this 'a':
[tex]a=7,217[/tex]The rate of decline for the population is 8.4% per year, this will be 'r':
[tex]r=8.4[/tex]Converting this amount from percentage to decimal number:
[tex]\begin{gathered} r=8.4/100 \\ r=0.084 \end{gathered}[/tex]And we require to find the number of cheetahs in 23 years, this will be the time 't':
[tex]t=23[/tex]Step 2. This problem is an example of exponential decay, and the formula to use is:
[tex]y=a(1-r)^t[/tex]Where 'y' represents the final amount after time t.
Step 3. Substituting the known values:
[tex]y=7,217(1-0.084)^{23}[/tex]Step 4. Solving the operations:
[tex]y=7,217(0.916)^{23}[/tex][tex]y=7,217(0.132921702)[/tex]The result is:
[tex]y=959.296[/tex]Rounding this result to the nearest whole number:
[tex]y=959[/tex]The prediction is 959 African cheetahs.
Answer: 959
