I not really understand that can you help me please ? 1.

a countrys population in 1992 was 72 million in 1998 it was 76 million estimate the population in 2012 using the exponential gro

crimeas [40]

Hi there
First find the rate of growth between
1992 and 1998
The formula is
P=Ae^rt
P the population in 1998. (76 million)
A the population in 1992 (72 million)
E constant
R rate of growth?
T time 1,998−1,992=6 years
We need to solve for r
R=[log (p/A)÷log (e)]÷t
R=(log(76÷72)÷log(e))÷6
R=0.009

Now find the population in 2012
P=Ae^rt
P ?
A 72 million
R 0.009
T 2,012−1,992=20 years
So
P=72×e^(0.009×20)
P=86.2 round your answer to get
P=86 million

Good luck!

5 0

2 years ago

A ball is thrown vertically upwards from the ground. It rises to a height of 10m and then falls and bounces. After each bounce,

Citrus2011 [14]

${\huge{\fcolorbox{yellow}{red}{\orange{\boxed{\boxed{\boxed{\boxed{\underbrace{\overbrace{\mathfrak{\pink{\fcolorbox{green}{blue}{Answer}}}}}}}}}}}}}$

(i)

$\sf{a_n = 20 \times {( \frac{2}{3} )}^{n - 1} }$

(ii)

$\sf S_n = 60 \{1 - { \frac{2}{3}}^{n} \}$

Step-by-step explanation:

$\underline\red{\textsf{Given :-}}$

height of ball (a) = 10m

fraction of height decreases by each bounce (r) = 2/3

$\underline\pink{\textsf{Solution :-}}$

(i) We will use here geometric progression formula to find height an times

${\blue{\sf{a_n = a {r}^{n - 1} }}} \\ \sf{a_n = 20 \times { \frac{2}{3} }^{n - 1} }$

(ii) here we will use the sum formula of geometric progression for finding the total nth impact

$\orange {\sf{S_n = a \times \frac{(1 - {r}^{n} )}{1 - r} }} \\ \sf S_n = 20 \times \frac{1 - ( { \frac{2}{3} })^{n} }{1 - \frac{2}{3} } \\ \sf S_n = 20 \times \frac{1 - {( \frac{2}{3}) }^{n} }{ \frac{1}{3} } \\ \sf S_n = 3 \times 20 \times \{1 - ( { \frac{2}{3}) }^{n} \} \\ \purple{\sf S_n = 60 \{1 - { \frac{2}{3} }^{n} \}}$