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

f(x) =
`3^(x)` + 10

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

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

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