Answer:
[tex]a.\ \ \ y=23.3e^{0.09902t}\\\\b.\ \ \ 38.23\ mg[/tex]
Step-by-step explanation:
-This is an exponential relationship where one of the variables contains an exponent component.
The general form of an exponential function is given as:
[tex]A_n=A_oe^{rt}[/tex]
where:
[tex]r-rate \ of \ growth/decay\\t-time\\A_o-Initial \ Population\\A_{t/n}-Population \ at \ time\ t/n[/tex]
#Given the initial population as 23.3mg, doubling time as 7hrs, we determine the growth rate as:
[tex]y=23.3e^{7r}\\\\y=23.3\times 2=46.6\\\\\therefore 2=e^{7r}\\\\7r=In \ 2\\\\r=0.09902[/tex]
#Substitute r in the general equation for solving for amount at time t:
[tex]y=23.3e^{0.09902t}[/tex]
b. We use the amount at time t from a above,[tex]y=23.3e^{0.09902t}[/tex], to calculate the amount after 5hrs as:
[tex]y=23.3e^{0.09902t}\\\\=23.3^{0.09902\times 5}\\\\=38.23\ mg[/tex]
Hence, the mass of the substance after 5hrs is 38.23 mg