A colony of insects grows exponentially from 100 to 146 in one week. How many DAYS does it take for the population to reach 1300?

Question

amistre64 · Answer

146/100 = 1.46; so it inceases at 146% in 7 days eh....

amistre64 · Answer

or is that 46% :)

yuki · Answer

You do something similar with the ozone one
let me just leave the formula since amistre can help you with the concept$$N_t = N_0(1.46)^{t/7}$$

amistre64 · Answer

7 days = 1/2x{0} + x{0} = x{n+1}

x{1} = 100(1.5) = 150

x{2} = 150(1.5) = ......is that what i was missing last time the 1?

amistre64 · Answer

...... good job yuki :)

anonymous · Answer

Ok, so the equation should look like 1300= 100(1.46)^(t/7).....right?

amistre64 · Answer

yes

anonymous · Answer

moving on, I should get to (log 13/log 1.46) = t/7.......right?

anonymous · Answer

Which gives me 47.44, so the answer is c?

anonymous · Answer

c is 47, sorry I forgot its not on here

yuki · Answer

remidia, since I don't know what the answer choices are I cannot say this by 100%, but it takes exactly 7*ln13/ln1.46 days to reach 1300.  Which means that if it is any less than that you still haven't reached 1300.

so, if there, by any chance, were two solutions 47 days or 48 days, make sure to pick 48 days, ok ?

anonymous · Answer

Ok, thank you!