The table below shows the balance B in a savings account, in dollars, in terms of time T$,$ measured as the number of years since the initial deposit was made.

Time t

$0$

$1$

$2$

$3$

$4$

Balance B

$120\mathrm{.}00$

$126\mathrm{.}00$

$132\mathrm{.}30$

$138\mathrm{.}92$

$145\mathrm{.}86$

$($a$)$ Was the yearly interest rate constant over the firsr four years?

Yes

No

If so$,$ find the rate $($Round your answer to two decimal places. If the rate is not constant, enter NONE.$)$

Explain why the rate is constant, or why it is not.

$($b$)$ Estimate B$(1\mathrm{.}50).($Assume that interested is compounded and deposited continuously. Round your answer to two decimal places.$)$

B$(1\mathrm{.}50)=$

Explain in practical terms what your answer means.

The account balance after $\_$ and $\_$ months is approximately $ $\_.$