A study is done on the population of a certain fish species in a lake. Suppose that the population size P(1) after years is given by the following exponential function.
P(t) = 400(1.22)
Find the initial population size.
Does the function represent growth or decay?
O growth O decay
By what percent does the population size change each year?

(1) A decay

(2) 22%

Step-by-step explanation:

(1)

This is an exponential function.

The number been raised to the power of time is a fraction which is less than 1. This means that as the time increases the fraction is decreasing hence the population.

(2)

The formula for getting the population is P(t)=420×〖0.78〗^t

This means that the current population is 420 and 0.78 is the percentage.

This will be equal to 0.78=78/100

As a percentage =78/100×100=78%

This means that the population decrease by (100-78) = 22%

(1st) A decay

(2nd) 22%

Step-by-step explanation:  

(1st)

The number has been raised to the power of time is a fraction which is less than 1. This means that as time increases the fraction is decreasing hence the population.

(2nd)

The formula for getting the population is P(t)=420×〖0.78〗^t

This means that the current population is 420 and 0.78 is the percentage.

This will be equal to 0.78=78/100

=78/100×100=78%

(100-78) = 22%  

191 students play sports and ninety-seven 10th graders were surveyed.

step-by-step explanation:

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: