Answer:
Please check the explanation.
Step-by-step 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:
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:
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
[tex]\frac{100\cdot \:2^x}{100}=\frac{6400}{100}[/tex]
Simplify
[tex]2^x=64[/tex]
[tex]\:2^x=2^6[/tex] ∵ 2⁶ = 64
[tex]x=6[/tex]
Therefore, in 6 hours i.e. x = 6 h, the number of cells present will be 6400.
