Question

Please I really need help(Logarithms):
The weight of bacteria in a culture t hours after it has been established is given by W=2.5x2^0.04t grams.
After what time will the weight reach 4 grams?

Answer 1

I tried solving it like this:
log4=log2.5 x 0.04t x log2
And then I just solved the equation but I keep getting it wrong

Answer 2

Thanks for your help :) I'll just check if it's right

Answer 3

okay the thing is we are just supposed to use base 10

Answer 4

and the answer is 17 but I get something else

Answer 5

\[2.5\times 2^{0.04t}=5\]
\[2^{0.04t}=2\]
\[.04t=1\]
\[t=1\div.04\]

Answer 6

oooh it said 4, not 5, my mistake

Answer 7

\[2.5\times 2^{.04t}=4\]
\[2^{.04t}=1.6\]
\[.04t=\frac{\ln(1.6)}{\ln(2)}\]
\[t=\frac{\ln(1.6)}{.04\ln(2)}\]

Answer 8

If you're interested in knowing the correct solution:

Answer 9

4=2.5x2^0.04t

Using the rules of the logarithms to expand this equation gives after a few steps

log4 = log2.5 + 0.04t x log2

Now solve this for t to get

t=(log4 - log2.5)/(0.04xlog2) = 16.95 or approx. 17.0 h