Question

Scientists released 10 birds into a new habitat in year 0. Each year, there were
three times as many birds as the year before. How many birds were there
after x years? Write a function to represent this scenario.

Answer 1

Answer:

f(x) = $3^{x}$ + 10

Step-by-step explanation:

Year one would be 10 + 3

Year two would be (3*3)+10

year three would be (3*3*3)+10

Which easily simplifies into $3^{x}$ + 10.

Answer 2

Answer:

The function can be written in Matlab program to compute the current number of birds in the habitat after x number or years.

f(x)=3ˣ*10

Step-by-step explanation:

From the question, in year zero we have 10 birds. This number increased to 30 on the first year.

0    Year     3⁰*10 = 10   Birds

1st   Year    3¹*10 = 30   Birds

2nd Year    3²*10 = 90  Birds

3rd  Year    3³*10 = 270 Birds

4th  Year     3⁴*10 = 810 Birds

xth   Year    3ˣ*10 = Current number of Birds

f(x) = 3ˣ*10

See below the MatLab function to solve the problem

   function NumOfBirds=currentbirds(x);%function to compute current number of birds in x number of years

   prompt='enter number of years in digits:  ';% This prompt you to input the number of years

   x=input(prompt);

   NNOB=3^(x)*10;% This compute the new number of birds in the habitat

   b=['The current number of birds is:  ',num2str(NNOB)];

   disp(b)% this display the result of the computation

SEE BELOW RESULT OF THE FUNCTION WHEN TESTED

>> currentbirds

enter number of years in digits:  3

The current number of birds is:  270

>> currentbirds

enter number of years in digits:  5

The current number of birds is:  2430

>> currentbirds

enter number of years in digits:  4

The current number of birds is:  810

>> currentbirds

enter number of years in digits:  10

The current number of birds is:  590490