Which function represents exponential decay? f(x) = one-half(2)x f(x) = three-fourths(negative one-fifth)x f(x) = 3(seven-halves)x f(x) = 2(two-thirds)x

A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.

We will see that the correct option is:

The form of the general exponential decay is:

f(x) = A*(r)^x

Where A is the initial value, x is the variable, and r is the rate at which it decreases, where r must be a number between 0 and 1.

The given options are:

Because r must be between zero and one, the only option that meets that requirement is the last one, where r = 2/3.

Then the function that represents an exponential decay is the last one:

If you want to learn more, you can read:

link

Step-by-step explanation:

We know that the exponential decay equation is given by :-

, where A = initial value.

b = Multiplicative growth rate  ( b <1 for decay)

x= time period.

Note : b ≠1 and b>0.

Let's check all the functions:

, here b =2 >1 , so this function does not represent exponential decay.

here b =  but b should be greater than 0 for exponential function, so this function does not represent exponential decay.

Here , , so this function does not represent exponential decay.

Here ,  , so this function represents exponential decay.

Hence, the correct answer is .

pls ask

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.