Answer:
<em>Math will take over Ana's brain at 4.4 hours</em>
Step-by-step explanation:
<u>Exponential Grow </u>
The population of the nanobots follows the equation
We must find the value of t such that the population of nanobots is 106 or more, that is
We'll solve the equation
Dividing by 5
Taking logarithms
By logarithms property
Solving for t
Math will take over Ana's brain at 4.4 hours
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Work Shown:
Check out the diagram below. Note the pair of alternate interior angles that are congruent (each 37 degrees). Then focus on triangle ABC. With the reference angle being at A, this means we use the tangent function because BC = x is the opposite side and AB = 97 is the adjacent side.
tan(angle) = opposite/adjacent
tan(A) = BC/AB
tan(37) = x/97
97*tan(37) = x
x = 97*tan(37)
x = 73.094742859971
For the last step, you'll need a calculator that can handle trig functions. Make sure the calculator is in degree mode. The result here is approximate. This rounds to 73 when rounding to the nearest whole number.
