Since the creation of a social program, the percent of persons $65$ years and over with a family income below the poverty level has declined. The percent can be

approximated by the function $P(t)=30\mathrm{.}51-5\mathrm{.}81lnt,$ where $t$ is the number of years since $1965.$ Answer parts a$.$ through $d.$ below.

a$.$ Find the percent of persons $65$ years and over with family income below the poverty level and the rate of change in $1970.$

The percent of persons $65$ years and over with family income below the poverty level in $1970$ was

$$

enter your response here$\%.$

$($Round to two decimal places as$$ needed.$)$

Part $2$

The rate of change of the percent of persons $65$ years and over with family income below the poverty level in $1970$ was

$$

enter your response here$\%.$

$($Round to four decimal places as$$ needed.$)$

Part $3$

b$.$ Find the percent of persons $65$ years and over with family income below the poverty level and the rate of change in $1990.$

The percent of persons $65$ years and over with family income below the poverty level in $1990$ was

$$

enter your response here$\%.$

$($Round to two decimal places as$$ needed.$)$

Part $4$

The rate of change of the percent of persons $65$ years and over with family income below the poverty level in $1990$ was

$$

enter your response here$\%.$

$($Round to four decimal places as$$ needed.$)$

Part $5$

c$.$ Find the percent of persons $65$ years and over with family income below the poverty level and the rate of change in $2010.$

The percent of persons $65$ years and over with family income below the poverty level in $2010$ was

$$

enter your response here$\%.$

$($Round to two decimal places as$$ needed.$)$

Part $6$

The rate of change of the percent of persons $65$ years and over with family income below the poverty level in $2010$ was

$$

enter your response here$\%.$

$($Round to four decimal places as$$ needed.$)$

Part $7$

d$.$ What happens to the rate of change over$$ time?

A$.$

The rate of change over time is approaching $0.$

B$.$

The rate of change over time is approaching minusinfinity.

C$.$

The rate of change over time is approaching infinity.