a) let t be the number of bacteria as its instructing you, A be the starting point, r be the rate of increment and T be time.
lets use the formula t=A\times r^T
T itself can be broken down into 2 components -- the 40 minutes were stated, and another unknown value which would be the time you want it to be; so: $ t=\frac{T_m}{40} $
respectively, substitute the values in:
$ t=1000\times 2^{\frac{T_m}{40}} $
b) we are working in minutes so one hour is equal to 60 minutes ; just plug that as T_m
$ t=1000\times 2^{\frac{60}{40}} $
$t\approx 1000\times 2.828 $
$t\approx 2828 $
c) its stated that $ t=(50000 +m)$ where $m=8$
$(50000 +8)=1000\times 2^{\frac{T_m}{40}} $ thus,
$50008=1000\times 2^{\frac{T_m}{40}}$
get rid of the base
$ 2^{\frac{T_m}{40}}=\frac{6251}{125} $
$ \frac{T_m}{40}\ln \left(2\right)=\ln \left(\frac{6251}{125}\right) $
$ T_m=225.7 $
d) use desmos, or try manually graphing it.
