calculus question

Question

A bacterial culture has an initial population of 10,000.  If its population declines to 4000 in 6 hours, when will its population be 2947?  Assume that the population decreases according to the exponential model.

a) after 9 hours

b) after 5 hours

c) after 8 hours

d) after 7 hours

Answer 1

0.4 = e^6k

ln 0.4 = 6k

-0.91629 ≈ 6k

-0.15272 ≈ k

0.2947 = e^-0.15272t

Can you calculate and answer?

Answer 2

4,000=10,000e^r(6)

.4 = e^6r

ln.4 = 6r

r = ln.4/6 = -.1527 = 15.27% reduction per hour

2947=10,000e^-.1527t

.2947 = e^-.1527t

ln.2947 = -.1527t

t = ln.2947/-.527 = 8 hours

A=10,000e^-.1527(9) = 2530

A=10,000e^-1527(5)= 4660

A=10,000e^-1527(8) = 2947

A=10,000e^-.1527(7) = 3434