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b

c

$A(t)=2000(1+0.04)_{t}$

Substitute$A(t)=2500$

$2500=2000(1+0.04)_{t}$

Solve for $t$

DivEqn$LHS/2000=RHS/2000$

$45 =(1+.04)_{t}$

AddTermsAdd terms

$45 =(1.04)_{t}$

$g(LHS)=g(RHS)$

$g45 =g(1.04)_{t}$

$g(a_{m})=m⋅g(a)$

$g45 =tg1.04$

DivEqn$LHS/g1.04=RHS/g1.04$

$g1.04g45 =t$

SimpQuotSimplify quotient

$5.69=t$

RearrangeEqnRearrange equation

$t=5.69$

d

$A(t)=2000(1+0.04)_{t}$

Substitute$A(t)=3000$

$3000=2000(1+0.04)_{t}$

Solve for $t$

DivEqn$LHS/2000=RHS/2000$

$23 =(1+.04)_{t}$

AddTermsAdd terms

$23 =(1.04)_{t}$

$g(LHS)=g(RHS)$

$g23 =g(1.04)_{t}$

$g(a_{m})=m⋅g(a)$

$g23 =tg1.04$

DivEqn$LHS/g1.04=RHS/g1.04$

$g1.04g23 =t$

SimpQuotSimplify quotient

$10.34=t$

RearrangeEqnRearrange equation

$t=10.34$