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# Exponentaial Function Question

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Miriam and Jessica are growning bacteria in a laboratory. Miriam uses the growth function f(t)=n2t while Jessica uses the function g(t)=n4t , where n repersents the initial number of bacteria and t is the time, in hours. If Miriam starts wiith 16 bacteria, how many bacteria should Jessica start with to achieve the same growth over time? Show work to support your answer.

Signed FRUSTRATED 7TH GRADE ALGEBRA 1 STUDENT WHO IS DOING HIS HOMEWORK NOW.

Mar 2, 2018

#1
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Miriam starts with   16^2t      And J starts with n^4t    and we want these to be equal.....

Sooooo let's set them equal and solve for n    the amount of bacteria Jessica needs

16^2t  = n ^4t         Log both sides to get

2t log16  = 4t log n  divide by 2t

log16 = 2 log n        divide by 2

(log 16 )/2 = log n    10 power both sides

10^((log16)/2) = n = 4   the number J needs to start with to keep things equal

Mar 2, 2018
#2
+15350
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Maybe a little easier way

16 ^2t  = n ^4t

(4^2)^2t = n^4t

4^4t = n^4t         so n = 4

Mar 2, 2018