in a study during the 1970s, it was found that one model of legislative turnover in the country a parliament…

in a study during the 1970s, it was found that one model of legislative turnover in the country a parliament was described by the following formula. m(t)=439e - 0.09t in this formula m(t) was the number of continuously - serving members at time t. here, t = 0 represents 1965, t = 1 represents 1966, and so on. use this model to approximate the number of continuously serving members in each year. (a)1969 (b)1975 (c)1980 (a) find the number of continuously serving members in 1969. (round to the nearest whole number as needed.)

in a study during the 1970s, it was found that one model of legislative turnover in the country a parliament was described by the following formula. m(t)=439e - 0.09t in this formula m(t) was the number of continuously - serving members at time t. here, t = 0 represents 1965, t = 1 represents 1966, and so on. use this model to approximate the number of continuously serving members in each year. (a)1969 (b)1975 (c)1980 (a) find the number of continuously serving members in 1969. (round to the nearest whole number as needed.)

Answer

Explanation:

Step1: Determine the value of t for 1969

Since t = 0 represents 1965, for 1969, t=1969 - 1965=4.

Step2: Substitute t into the formula

Substitute t = 4 into M(t)=439e^{- 0.09t}. So M(4)=439e^{-0.09\times4}. First, calculate -0.09×4=-0.36. Then e^{-0.36}=\frac{1}{e^{0.36}}. Using a calculator, e^{0.36}\approx1.433329, so \frac{1}{e^{0.36}}\approx0.697676. Then M(4)=439×0.697676.

Step3: Calculate the result

M(4)=439×0.697676\approx306.38. Rounding to the nearest whole - number, M(4)\approx306.

Answer:

306