Answer:
t = 5.59x10⁴ y
Explanation:
To calculate the time for the ¹⁴C drops to 1.02 decays/h, we need to use the next equation: 
 (1)
    (1)
<em>where  : is the number of decays with time, A₀: is the initial activity, λ: is the decay constant and t: is the time.</em>
: is the number of decays with time, A₀: is the initial activity, λ: is the decay constant and t: is the time.</em>
To find A₀ we can use the following equation:  
 (2)
   (2)
<em>where N₀: is the initial number of particles of ¹⁴C in the 1.03g of the trees carbon </em>
From equation (2), the N₀ of the ¹⁴C in the trees carbon can be calculated as follows:        
 
 
<em>where  : is the tree's carbon mass,
: is the tree's carbon mass,  : is the Avogadro's number and
: is the Avogadro's number and  : is the ¹²C mass.  </em>
: is the ¹²C mass.  </em>
 
    
Similarly, from equation (2) λ is:
 
 
<em>where t 1/2: is the half-life of ¹⁴C= 5700 years </em>

So, the initial activity A₀ is:   
 
     
Finally, we can calculate the time from equation (1):
 
               
I hope it helps you!