Question

Replace the values of A, b, x, and y to write an exponential equation that represents the number of cells present at h hours.

Answer 1

Please check the explanation.

Explanation:

Given the table

Time, x(hours) Number of Cells, y

0 100

1 200

2 400

h 6400

We know that the exponential function is of the form

A(b)ˣ = y

substituting x = 0 and y = 100

A(b)⁰ = 100

A×1 = 100 ∵ (b)⁰ = 1

substituting x = 1 and y = 200

A(b)¹ = 200

Ab = 200

plug in A = 100

100×b = 200

b = 200/100

b = 2

So, the values of A and b are:

• A = 100

• b = 2

Thus, the equation of the exponential function becomes:

A(b)ˣ = y

substituting A = 100 and b = 2

100(2)ˣ = y

Thus, the equation of the exponential function becomes:

• 100(2)ˣ = y

Given that we have to determine the value of 'h' hours at y = 6400

so substituting y = 6400

100(2)ˣ = y

100(2)ˣ = 6400

divide both sides by 100

`(100\cdot \:2^x)/(100)=(6400)/(100)`

Simplify

`2^x=64`

`\:2^x=2^6` ∵ 2⁶ = 64

`x=6`

Therefore, in 6 hours i.e. x = 6 h, the number of cells present will be 6400.