As a town gets smaller, the population of itd high school decreases by 7% each year. the senior class has 160 students now in how many years will it have about 100 students? write an equation. then solve the equation without graphing. its not 13

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

Step-by-step 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