Answer
a. $2249.73$
b. $4051.63$
c. $6$ years
d. $11$ years
Work Step by Step
$A(t)=a(1+r)^t$
a = 2000
r = 4% = 0.04
a. A(t) = ?
t = 3 years
Substituting values
A(t) = 2000(1+0.04)^{3}
A(t) = 2000(1.04)^{3}
A(t) = 2000(1.12)
$A(3) = 2249.73$
b. A(t) = ?
t = 18 years
Substituting values
A(t) = 2000(1+0.04)^{18}
A(t) = 2000(1.04)^{18}
A(t) = 2000(2.02)
$A(18) = 4051.63$
c. A(t) = 2500
t = ?
Substituting values
2500 = 2000(1+0.04)^{t}
1.25 = (1.04)^{t}
Using the definition of logarithm
log_{1.04}1.25 = t
$t=5.7 \approx 6$ years
d. A(t) = 3000
t = ?
Substituting values
2500 = 3000(1+0.04)^{t}
1.5 = (1.04)^{t}
Using the definition of logarithm
log_{1.04}1.5 = t
$t=10.34 \approx 11$ years
