At the end of the Year 1 the population will be = 110,000 + 4% of 110,000 =P1At the end of the Year 2 the population will be=P1+ 4% of P1= 110,000 + 4% of 110,000 + 4% of (110,000 + 4% of 110,000) = 110,000 + 4% of (110,000+ 110,000 + 4% of 110,000) = 110,000 + 2*4% of 110,000 + (4%)2 of 110,000= P2At the end of the Year 3 the population will be= P2+ 4% of P2= 110,000 +2* 4% of 110,000 + (4%)2 of 110,000 + 4% of [ 110,000 +2* 4% of 110,000 + (4%)2 of 110,000] = 110,000 +2* 4% of 110,000 + (4%)2 of 110,000 + 4% of 110,000 + 2* (4%)2 of 110,000 + (4%)3 of 110,000 =110,000 +3* 4% of 110,000 +3* (4%)2 of 110,000 + (4%)3 of 110,000 =P3At the end of the Year 4 the population will be= P3+ 4% of P3=110,000 +3* 4% of 110,000 +3* (4%)2 of 110,000 + (4%)3 of 110,000 +4% of [110,000 +3* 4% of 110,000 +3* (4%)2 of 110,000 + (4%)3 of 110,000] =110,000 +4* 4% of 110,000 + 6*(4%)2 of 110,000+4* (4%)3 of 110,000+ (4%)4 of 110,000 Now if we substitute n for 110,000 and r for 4% yearly rate of increase, we can rewrite,Before Year 1, at Year 0, the population, P0= n = n(1+r)0At the end of the Year 1 the population , P1= n+rn= x(1+r)1At the end of the Year 2 the population , P2= n+2rn+r2n =n(1+2r+r2)=n(1+r)2At the end of the Year 3 the population , P3= n+3rn+2r2n+r3n=n(1+3r+3r2+r3)=x(1+r)3At the end of the Year 4 the population , P4= n+4rn+6r2n+4r3n+r4n=n(1+r)4.
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At the end of the Year n the population , Px=n+nrx+(x-1)r2n+(x-2)r3n+...........+(x-x+2)r(x-1)x+(x-x+1)rxn=n(1+r)x.....At the end of the Year 16 the population , P16= n+16rn+15r2n+14r3n+.............+3r14n+2r15n+r16n=n(1+r)16 Thus under given condition of rate of growth, the Population P(x) at xth year will be P(x)=n(1+r)x Therefore, a population of 110,000 growing at 4% per year, in 16 years will be= 110,000(1+4/100)16= 110,000(1.04)16=206027.93702999115428132473599427≈206028
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Answer:
H1 : μ < 1225
Step-by-step explanation:
The alternative hypothesis in carrying out a statistical test could be explained as a notion which aims to displace or rival an initial position, the null hypothesis.
When declaring an hypothesis, the statement compares the initial or population mean in the hypothesis statement and not the result or outcome of the sample statistic.
In the scenario above :
The null is of the notion that :
H0 : μ = 1225 ;
Hence, the stance of the alternative which is that the mean is lower or less will be written as :
H1 : μ < 1225
