Answer:
a) 16.82 mg
b) 24 days
Step-by-step explanation:
Formula for exponential growth is given as:
[tex]A=A_0b^{\frac{t}{c}}[/tex]
Where A is the final population
[tex]A_0[/tex] is the initial population
b is the growth factor
c is the time taken for the growth 'b'
t is the amount of time
Here, We are given the following:
[tex]A_0[/tex] = 5 mg
b = 2 (Given because it doubles)
c = 4 days
a) A = ?
Using the formula:
[tex]A=5 \times 2^{\frac{7}{4}}\\\Rightarrow A=5 \times 2^{1.75} \\\Rightarrow A = \bold{16.82\ mg}[/tex]
b) Given
A = 320 mg
t = ?
Using the above formula again:
[tex]320 = 5 \times 2^{\frac{t}{4}}\\\Rightarrow \dfrac{320} 5= 2^{\frac{t}{4}}\\\Rightarrow 2^{\frac{t}{4}} = 64\\\Rightarrow 2^{\frac{t}{4}} = 2^6\\\Rightarrow \dfrac{t}{4} = 6\\\Rightarrow t = 6 \times 4\\\Rightarrow \bold{t = 24\ days}[/tex]
So, the answers are:
a) 16.82 mg
b) 24 days
