anonymous
  • anonymous
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? A) 39 days B) 43 days C) 47 days D) 51 days E) 55 days
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
100 + x^7 = 146
amistre64
  • amistre64
x^7 = 46 x = 46^(1/7) right?
anonymous
  • anonymous
Correct.. can I ask how you got the first equation?

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amistre64
  • amistre64
the first equationis the inital value then simply add the exponential growth to it
amistre64
  • amistre64
we know that it starts at 100 so.. 100 +..... add the exponential growth in at 7days 100 + x^7.....now that should equal 146 my exponential part my be in error, but its basically that
amistre64
  • amistre64
the exponent i believe is measured in time units... to we need to calibrate it for the base unit....is my reasoning for picking x^7
amistre64
  • amistre64
soo.... 100 + 46^(1/7)^d = 1300 ; where d is in days 46^(d/7) = 1200 d/7 log(46) = log(1200) d/7 = log(1200)/log(46) d = 7(log1200)/log(46)
amistre64
  • amistre64
d = 12.96 days if we do it that route...gotta adjust for my stupidity herelol...hold on
amistre64
  • amistre64
ack!!...thats it if i did it right; but apparently i messed up in the exponential department ;)
amistre64
  • amistre64
x{n+1} = ax{n} + b .... recurrsion formulas, the bane of my existence

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