Question

The problem is in the picture, I just need the answer

Answer 1

we are given the following formula for the balance of a bank account:

`f(t)=10e^(0.07t)`

a. The opening balance is given when the value of the time "t" is zero, that is t = 0:

`\begin{gathered} f(0)=10e^(0.07(0)) \\ f(0)=10 \end{gathered}`

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":

`1000000=e^(0.07t)`

Taking natural logarithm on both sides:

`\ln 1000000=0.07t`

Dividing both sides by 0.07:

`(1)/(0.07)\ln 1000000=t`

Solving the operation:

`197.4=t`

Therefore, the balance will be 1000000 in 197.4 years.