Answer:
a=55
b=5
T=17
Step-by-step explanation:
The general form of the equation is:
[tex]N(t)=ab^{\frac{t}{T}}[/tex]
For t = 0:
[tex]N(0)=ab^{\frac{0}{T}}\\N(0) = a = 55\\a=55[/tex]
Since there has been a fivefold increase after 17 years, at t = 17, N(17) = 55*5
[tex]N(17)=55b^{\frac{17}{T}}\\55*5 = 55b^{\frac{17}{T}}\\b^{\frac{17}{T}} = 5[/tex]
If at every 17*n years there in an increase of 5^n, one can deduct that the values for T and b are respectively 17 and 5:
[tex]b^{\frac{t}{T}}= 5^{\frac{17n}{17}}[/tex]
Therefore, the function that represents N(t) is:
[tex]N(t)=55*5^{\frac{t}{17}}[/tex]
