Answer:
B.2152
Step-by-step explanation:
To solve this we are using the standard exponential growth equation:
[tex]y=a(1+b)^x[/tex]
where
[tex]y[/tex] is the final value after [tex]x[/tex] years
[tex]a[/tex] is the initial value
[tex]b[/tex] is the growing rate in decimal form
[tex]x[/tex] is the time in years
We know from our problem that the GNP is growing 4.8% per year, so [tex]b=\frac{4.8}{100} =0.048[/tex]. We also know that the GDP in 1994 was $5.9 billion and the desired GNP is $10 trillion, so [tex]a=5,900,000,000[/tex] and [tex]y=10,000,000,000,000[/tex].
Replacing values
[tex]y=a(1+b)^x[/tex]
[tex]10,000,000,000,000=5,900,000,000(1+0.048)^x[/tex]
[tex]10,000,000,000,000=5,900,000,000(1.048)^x[/tex]
Divide both sides by 5,900,000,000:
[tex]\frac{10,000,000,000,000}{5,900,000,000} =(1.048)^x[/tex]
Take natural logarithm to both sides
[tex]ln(1.048)^x=ln(\frac{10,000,000,000,000}{5,900,000,000})[/tex]
[tex]xln(1.048)=ln(\frac{10,000,000,000,000}{5,900,000,000})[/tex]
Divide both sides by ln(1.048)
[tex]x=\frac{ln(\frac{10,000,000,000,000}{5,900,000,000})}{ln(1.048)}[/tex]
[tex]x[/tex] ≈ 158
We now know that Canada's GNP will reach $10 trillion after 158 years from 1994, so to find the year we just need to add 158 years to 1994:
1994 + 158 = 2512
We can conclude that the correct answer is B.2152
