Answer: [tex]a_n = 4(1.1)^{n-1}[/tex]
Step-by-step explanation:
Since, the initial number of hot dogs = 4
According to the question,
The number of hot dogs is increasing by 110% of that of previous day,
Thus, the number of hot dog in first day = 4
Second day = 110 % of 4 = 4.4
Third day = 110% of 4.4 = 4.84
Fourth day = 110% of 4.84 = 5.324
So on.......
Thus, we get a GP,
4, 4.4, 4.84, 5.324 ..........................
That having common ratio, d = 1.1
And, first term, a = 4
Since, the nth term of the GP, [tex]a_n = a\times d^{n-1}[/tex]
Hence, the required explicit formula of the given situation,
[tex]a_n = 4(1.1)^{n-1}[/tex]
Answer:
The number of hot dogs on any particular day is given by:
[tex]D_n=(1.1)^{n-1}\times 4[/tex] where n represents the nth day.
Step-by-step explanation:
Let [tex]D_n[/tex] represents the number of hot dogs in nth day of his training.
As it is given that he eats 4 hot dogs on his first day of training that means:
[tex]D_1=4[/tex]
Now it is also given that:
he plans to eat 110% of the number of hot dogs he ate the previous day.
i.e. the recurrence relation is given as:
[tex]D_n=110\%\times D_{n-1}[/tex]
which could also be written as:
[tex]D_n=1.1\times D_{n-1}[/tex]
Now:
[tex]D_2=1.1\times D_1=1.1\times 4\\\\D_3=1.1\times D_2=1.1\times 1.1\times 4=(1.1)^2\times 4\\\\D_4=1.1\times D_3=(1.1)^3\times 4\\\\.\\.\\.\\.\\.\\.\\D_n=(1.1)^{n-1}\times 4[/tex]
Hence, the number of hot dogs on any particular day is given by:
[tex]D_n=(1.1)^{n-1}\times 4[/tex] where n represents the nth day.
