Question

Pre-calc help please?

A skull cleaning factory cleans animal skulls of deer, buffalo, and other types of animals using flesh-eating beetles. The factory owner started with only 7 adult beetles. After 46 days, the beetle population grew to 21 adult beetles. How long did it take before the beetle population was 7,000 beetles?

Answer 1

same kind of problem right exponential growth

Answer 2

ok so a0 is the initial population of 7
a is the population of 7,000
t is the time it takes

Answer 3

\[(\ln(.7*10^3))/1*10^3*x=7000 ? \]

Answer 4

remember we derived this?

\[\ln(\frac{ a }{ a_{0} })*\frac{ 1 }{ t } = k\]

\[\ln(\frac{ 21 }{ 7 })*(\frac{ 1 }{ 46 }) = 0.02388 = k \]

Answer 5

\[7*e^{0.02388t} = a\]

Answer 6

we know that the final population is 7,000 so we need to solve for that

Answer 7

ok so 7*e^0.02388t=7000

Answer 8

yep, but what I like to do is solve for the variable i'm looking for then plug in

\[a_{0}e^{kt} = a \]

\[\ln(\frac{ a }{ a_{0} }) = kt \]

\[\ln(\frac{ a }{ a_{0} })*\frac{ 1 }{ k } = t \]

Answer 9

\[\ln (\frac{ 7,000 }{ 7 })*(\frac{ 1 }{ 0.02388 }) = t~days \]

Answer 10

ok i got 289 days

Answer 11

thanks!

Answer 12

excellent nice

Answer 13

but a good tip would be to solve the equation for the unknown variable first. then plug in