exponential functions

Question

A scientist counts 35 bacteria present in a culture and finds that the number of bacteria triples each hour. The function  models the number of bacteria after x hours. Estimate when there will be about 550 bacteria in the culture.

Answer 1

For exponential functions, the general equation is: y = initial*(multiplier)^time

In this case, the initial number of bacteria is 35. The multiplier is 3 (since bacteria triple in number every hour). The time is in the unit of hours.

550 refers to the y-value after a certain amount of time, which you're trying to solve for.

So, plug in 550 as y, 35 as initial, 3 as multiplier, and solve for x (time).

When solving for this equation, you will have to know how to manipulate logs.

First, divide both sides by 35.

Then, to get rid of the base 3, take log₃ on both sides of the equation. Then solve for x.

Answer 2

y = 35*3^x you want to solve for x, the exponent, given a y value. Therefore, use ln to bring down the exponent, x and solve for it:

ln(y) = ln(35) + x ln(3) Using product rule and exponent rule for logs.

You can insert y value and solve for x or you can represent by solving for x in terms of y and then plugging in.

Take care