i need a solutions for these question in Matlab thanks 8 Buil-in MATLAB Function

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i need a solutions for these question in Matlab
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8 Buil-in MATLAB Functions BLEMS Elementary Math Functions 3.1 Find the nearest integer of 3.3 and-3.3 by using both the fix and floor functions. Explain why there is a difference in the results of the fix and floor functions between the two cases in your answer. 3.2 MATLAB contains functions to calculate the natural logarithm (Log), the logarithm to the base 10 (log10), and the logarithm to the base 2 (log2). However, if you want to find a logarithm to another base-for example, base byou'll have to do the math yourself with the formula log,(x) log,(x) = Top.(by What is the log, of 10 when b is defined from 1 to 10 in increments of 1? 8.3 Populations tend to expand exponentially, that is, where P= current population P original population r continuous growth rate, expressed as a fraction t = time If you originally have 100 rabbits that breed at a continuous growth rate of 90% (r-0.9) per year, find how many rabbits you will have at the end of 10 years. Chemical reaction rates are 3.4 proportional to a rate constant k that changes temperature according to the Arrhenius equation For a certain reaction Q-8000 cal /rnol R 1.987 cal/mol K ko = 1200 min-1 Find the values of k for temperatures from 100 K to 500 K, in 50 increments. Create a table of your results. 3.5 Consider the air-conditioning requirements of the large home shown in Figure P3.5. The interior of the house is warmed by waste heat from lighting and electrical appliances, by heat leaking in from the outdoors, and by heat generated by the people in the home. An air-conditioner must be able to remove all this thermal energy in order to keep the inside temperature from rising. Suppose there are 20 light bulbs emitting 100 J/s of energy each and four appliances emitting 500 J/s each. Suppose also that heat leaks in from the outside at a rate of 8000 J/s (a) How much heat must the airconditioner be able to remove from the home per second?

Explanation / Answer

3.1) From the MATLAB function definitions, as fix rounds elements to the nearest integer towards zero, and floor rounds element to the nearest integer less than or equal to that element.
Thus for positive numbers, both of them would become the same answer as for the case of x=3.3
fix(x)=3, as 3 is the nearest integer for x towards zero and and floor(x)=3, as 3 is the nearest integer less than x.
But for negative numbers, both of them would differ by 1, as for the case of y=-3.3
fix(y)=-3, as -3 is the nearest integer for y towards zero and floor(y)=-4, as -4 is the nearest integer less than y.
The same can be checked from the MATLAB code:

clc;clear all;close all;
x=3.3;y=-3.3;
m=fix(x);n=floor(x);
p=fix(y);q=floor(y);
display(m);display(n);
display(p);display(q);

3.2) By implementing the following code in MATLAB, we can obtain the different values of logb(10) for b=1:10

clc;clear all;close all;
b=1:10;
for i=1:length(b)
ans(i)=log(10)./log(b(i));
end
display(ans);

Result: for b=1 : 10
answer = Inf 3.3219 2.0959 1.6610 1.4307 1.2851 1.1833 1.1073 1.0480 1.0000

3.3)By implementing the equation in MATLAB we get:

clc;clear all;close all;
P0=100;r=0.9;t=10;
P=P0.*(exp(r.*t));
display(P);

Result: P = 810308.3927575385 (accurate) = 810308 rabbits (approximate)

3.4) By implementing the following code in MATLAB we can obtain the values of k:

clc;clear all;close all;
T=100:50:500;Q=8000;R=1.987;k0=1200;
k=k0.*(exp((-Q)./(R.*T)));
display(k);

3.5) Question is incomplete, as the figure mentioned in the question is not given(Figure P3.5).

T-values k-values 100 3.92E-15 150 2.64E-09 200 2.17E-06 250 0.000121621 300 0.00178116 350 0.01211554 400 0.051029651 450 0.15614537 500 0.382027236

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