The table below represents an exponential function. what is the missing value?

The missing value is 128

Step-by-step explanation:

we know that

The equation of the exponential function is of the form

where

a is the initial value (value of the function when the value of x is equal to zero)

b is the base

r is the rate

b=(1+r)

In this problem , looking at the table, we have that  the number of bacteria is doubled every second

so

substitute in the formula

where

f(x) is the number of bacteria

x is the time in seconds

For x=4 sec

substitute

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places