Answer:23.8
Step-by-step explanation:Exponential Functions:
y, equals, a, b, to the power x
y=ab
x
a, equals, starting value = , 6300
a=starting value = 6300
r, equals, rate = , 6, point, 5, percent, equals, 0, point, 0, 6, 5
r=rate = 6.5%=0.065
Exponential Growth:
Exponential Growth:
b, equals, 1, plus, r, equals, 1, plus, 0, point, 0, 6, 5, equals, 1, point, 0, 6, 5
b=1+r=1+0.065=1.065
Write Exponential Function:
Write Exponential Function:
y, equals, 6300, left bracket, 1, point, 0, 6, 5, right bracket, to the power x
y=6300(1.065)
x
Put it all together
Plug in y-value:
Plug in y-value:
28200, equals, 6300, left bracket, 1, point, 0, 6, 5, right bracket, to the power x
28200=6300(1.065)
x
start fraction, 28200, divided by, 6300, end fraction, equals, start fraction, 6300, left bracket, 1, point, 0, 6, 5, right bracket, to the power x , divided by, 6300, end fraction
6300
28200
=
6300
6300(1.065)
x
Divide both sides by 6300
4, point, 4, 7, 6, 1, 9, equals, 1, point, 0, 65, to the power x
4.47619=1.065
x
log, 4, point, 4, 7, 6, 1, 9, equals, log, 1, point, 0, 65, to the power x
log4.47619=log1.065
x
Take the log of both sides
log, 4, point, 4, 7, 6, 1, 9, equals, x, log, 1, point, 0, 6, 5
log4.47619=xlog1.065
Use power rule to bring x to the front
start fraction, log, 4, point, 4, 7, 6, 1, 9, divided by, log, 1, point, 0, 6, 5, end fraction, equals, start fraction, x, log, 1, point, 0, 6, 5, divided by, log, 1, point, 0, 6, 5, end fraction
log1.065
log4.47619
=
log1.065
xlog1.065
Divide both sides by log(1.065)
23, point, 7, 9, 9, 5, 5, 7, equals, x
23.799557=x
x, approximately equals, 23, point, 8
x≈23.8