we are given the following formula for the balance of a bank account:
[tex]f(t)=10e^{0.07t}[/tex]
a. The opening balance is given when the value of the time "t" is zero, that is t = 0:
[tex]\begin{gathered} f(0)=10e^{0.07(0)} \\ f(0)=10 \end{gathered}[/tex]
Therefore, the initial balance is 10.
b. To determine when the balance reaches 1000000 we need to replace f(t) = 1000000 and solve for "t":
[tex]1000000=e^{0.07t}[/tex]
Taking natural logarithm on both sides:
[tex]\ln 1000000=0.07t[/tex]
Dividing both sides by 0.07:
[tex]\frac{1}{0.07}\ln 1000000=t[/tex]
Solving the operation:
[tex]197.4=t[/tex]
Therefore, the balance will be 1000000 in 197.4 years.
