Answer: The equation is 100 = 160*0.93^t which solves to t = 6.476 approximately. So it takes about 6.476 years for the senior class to go from 160 to 100
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Explanation:
The formula we are interested in is this
A = P*(1+r)^t
P is the initial population, A is the final population, r is the annual growth rate and t is the time in years.
In our case, A = 100, P = 160 and r = -0.07 (the negative indicating decrease)
Plug these values into the equation. Then solve for t
A = P*(1+r)^t
100 = 160*(1-0.07)^t
100 = 160*0.93^t
160*0.93^t = 100
0.93^t = 100/160
0.93^t = 0.625
log(0.93^t) = log(0.625) <<--- exponent in the trees, log it down
t*log(0.93) = log(0.625)
t = log(0.625)/log(0.93)
t = 6.476
This t value is approximate and rounded to 3 decimal places