How to predict the death rate in 1993

[fawazalusail]

The table shows the age-adjusted death rates (per 100,000 population) for heart disease in a certain country.

,,,,,,,Year|1970|1980|1990|1995|1997
DeathRate|253.5|197.4|153.7|135.6|129.0

Use the first and last data points to find an exponential function of the form f(t)=y0b^t where t is the time in years and t=0 in 1970. Then use the model to predict the death rate in 1993.
----------------------
f(0)=253.5
f(27)=129.0 <<<How did we get 27 :?:
y0b^0=253.5
y0=253.5
-
f(27)=129.0
253.5b^27=129.0
b^27=0.5089
b=0.9753
-
f(t) =253.5(0.9753)^23
=143

Thanks.

 

[srmichael]

The table shows the age-adjusted death rates (per 100,000 population) for heart disease in a certain country.

,,,,,,,Year|1970|1980|1990|1995|1997
DeathRate|253.5|197.4|153.7|135.6|129.0

Use the first and last data points to find an exponential function of the form f(t)=y0b^t where t is the time in years and t=0 in 1970. Then use the model to predict the death rate in 1993.
----------------------
f(0)=253.5
f(27)=129.0 <<<How did we get 27 :?: ====> 1997 - 1970. It's the difference in the years from the starting year, 1970, to the year that is 129, which is 1997.
y0b^0=253.5
y0=253.5
-
f(27)=129.0
253.5b^27=129.0
b^27=0.5089
b=0.9753
-
f(t) =253.5(0.9753)^23
=143

Thanks.

.

 

[fawazalusail]

Thanks a lot