SOLUTION: In a survey in 2000, the population of two plant species were found to be growing exponentially. Their growth is given by these equations: species A, P=2000e^0.05t and species B, P

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: In a survey in 2000, the population of two plant species were found to be growing exponentially. Their growth is given by these equations: species A, P=2000e^0.05t and species B, P      Log On


   

Question 135680: In a survey in 2000, the population of two plant species were found to be growing exponentially. Their growth is given by these equations: species A, P=2000e^0.05t and species B, P=5000e^0.02t, where t=0 in the year 2000.
Based on this information, after how many years will the population of species A be equal to the population of species B in the forest?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Given: P=2000e%5E0.05t+and+species+B%2C+P=5000e%5E0.02t t=0 in 2000
When do they equal??
2000e%5E0.05t+=+5000e%5E0.02t
e%5E0.05t+=+2.5e%5E0.02t
ln%28e%5E0.05t%29+=+ln%282.5e%5E0.02t%29
ln%28e%5E0.05t%29+=+ln%282.5%29+%2B+ln%28e%5E0.02t%29
0.05t+=+0.916+%2B+0.02t
0.03t+=+0.916
t+=+30.54 = June in the year 2030
Check your answer. Is 2000e%5E%280.05%2A30.54%29+=+5000e%5E%280.02%2A30.54%29 ???