The population (in millions) of a certain country t years after 1900 is given by the function p(t). there were 480 million in 1900. if p′(t)=3 throughout the time span 1900 to 1910, what was the population of the country in 1907? (hint: what was the practical signifigance of p′(t)=3 )

The population of the country in 1907 was 501 million.

Step-by-step explanation:

Hi there!

The population is given by the function p(t)

We know that p(0) = 480 million and that p´(t) = 3.

p´(t) is the derivative of the function p(t) and expresses the variation (or rate of change) of the population with respect to "t". In this case, p´(t) = 3 indicates that the population increases by 3 million per year (because t is in years) from 1900 to 1910. Then, in 1907 the population will be:

480 million + 3 million / year · 7 year = 501 million.

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

many reason,

step-by-step explanation: